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/ 

ANNUITIES 

and 

AMORTIZATION 

TABLES 

By PIERRE ZALDARI 


Price, $10.00 Net 


BANKERS ENCYCLOPEDIA CO. 

Publishers 
NEW YORK. 1917 




.'Z-'J 





COPYRIGHT 1917 
by 

BANKERS ENCYCLOPEDIA CO. 
New York 



/ 

■JAi'l 24 1918 


i 



©CI.A492()G8 



L- 


INTRODUCTORY NOTE 


It is a great honor to be asked by Mr. Pierre Zaldari to write an introduc¬ 
tory note to this edition of ANNUITIES and AMORTIZATION TABLES; and 
it is really a pleasure to comply with the request for, in so doing, we are intro¬ 
ducing at a most opportune time a book that is the product of over twenty 
years of active experience in international finance in several countries, and of 
several years of patient, careful computation. 

This pleasure is increased when we realize that in this small volume are 
given one hundred and four problems in simple statement, with a clear-cut 
exposition of the solution of each, and that these problems cover the whole range 
of type problems that arise in finance, that the tables are adequate to the 
solution of each and all these problems by a single multiplication, that the range 
of the several tables is greater than that of the corresponding tables that are 
found in other books, and that they are more minute in that the interest rates 
vary from % of 1% to 10 % by as little as and the periods go up to one 
hundred years. Some of the seven tables have no counterpart in other books. 

The financial world is to be congratulated on getting within the covers of 
a single small volume all the tables needed, whether in a bank, a bond house, a 
trust company, the offices of a large corporation or of municipal officials, in con¬ 
nection with sinking funds, loans, bonds, mortgages, etc.; and Mr. Zaldari is to 
be congratulated on producing a book of so wide and thorough usefulness. 


December, 1917. 


CHARLES C. GROVE 
Assistant Professor of Mathematics 
Columbia University of the City of New York 



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PREFACE 


The preparation of this work was suggested to the writer primarily by the 
more or less recent development of what may be called foreign financing in this 
country, and the greatly increased importance in the position which America has 
assumed as a factor in the general scope of international banking; and some of 
these tables and problems were prepared to meet the specific demands of the 
Federal Farm Loan Act in that section which provides that the Farm Loan 
Board “ shall prepare and publish amortization tables.” 

The method employed herein for the solution of the various problems is 
essentially different from that used in any other published work, and is so very 
simple that it requires only an elementary knowledge of arithmetic, well within 
the ability of every person using the rules herein applied to the conditions in¬ 
volved in every specific transaction. 

In order to enlarge the scope and the utility of this work, it was deemed 
especially desirable to avoid the use of all algebraic methods, as they are neces¬ 
sarily more complicated and are not so generally understood in their operations 
or so readily comprehended by the majority of accountants and bankers; and 
therefore all the operations herein are based upon simple arithmetic. 

The work may be divided into two distinct parts, 1st. the solution of the \ 
four fundamental problems of the calculation of Compound Interest; and 2nd. | 
Annuities, Amortization and Long Term loans. 

The preparation of Table I constitutes the essential foundation and is the 
pivot of the preparation of the other Tables. It has been checked every five 
years by using logarithms of seven figures, which are considered sufficient for 
all necessities in modem financial problems. 

The calculation of the problems in compound interest necessarily demands 
the use of logarithms to determine tf for a period of time. It is also possible to 
make this calculation in the ordinary arithmetical way, but it is not practicable 
because of the extremely laborious work entailed in such calculations. 

For the purpose of avoiding the continuous use of logarithms, which are 
not popular, the following elements are employed in the preparation of Table 1. 

Capital—C. Rate of interest—P. Time=A^. 


The amount to which a capital will increase, invested at compound in- 
terest=5. 

Expressed in algebraic form the equation reads: 

and changing 1+^^ q we have S=cq'", 

i.e. the value of $1. invested at a known rate of compound interest for a num¬ 
ber of years. 

Consequently this equation, composed of the four elements 5, C, Q, N, 
gives rise to the four problems :— 

3rd Q=V ^ 


1st S=cq^ 


2nd 


C=^ 


4th 

log q 


The First Table has been extended to include all the rates of interest and 
the periods of years to meet all requirements likely to arise in the financial 
problems of the present day. 

The same problem also demonstrates the equation C—the basis of the 

Fifth, Sixth, and Seventh Tables, viz.: to determine the capital C, or the actual 
value of an amount that will increase to 5, at compound interest for any given 
period of time, N. 

The Second Table is based upon the principle of the well-known geometric 


Therefore 5' 


r(c7^-l) 


q—l 


progression a-\-aq-\raq^-[-aq^ .... aq” ^ 

i.e. the unknown amount, or the amount of accumulated capital at compound inter¬ 
est, equals the annual income A multiplied by the unit $1, plus its interest for one 
year Q, raised to the power N, the number of years. 

The Third Table is based upon the following:— 

By the First Table a capital C, at compound interest for a period of time 
N, equals cq^. The annuity or annual investment A, at the end of a period of 

time N, equals > therefore, if A is the amount of annuity which will am¬ 
ortize a capital C in a period N, from which which 

is the equation for the Third Table. 









The Fourth Table has the same equation as the Third, with this difference, 
that the interest is compounded oftener than in yearly periods, ue, semi-annually; 
and therefore the annuity is likewise paid semi-annually. 

In the Second Table the method used is where the amount invested is 
repeated, i.e. the same amount of capital is added to the increasing capital at 
the end of each period. 

A study of the Tables will show the close correlation of the first three, as 
is further fully explained in Chapter III. 

Each chapter is also illustrated by specific tables, which explain the applica¬ 
tion of the principle involved in every one of the problems, thereby illuminating 
every feature of the Tables by giving the reader a comprehensive grasp of the 
practical utility of this work. 

PIERRE ZALDARI 

NOTE—Throughout the book in formulas caps or small letters are used 
ad libitum as a matter of convenience, and have the same significance in either 


case. 


V 


ANNUITIES AND AMORTIZATION TABLES 


CHAPTER I 


COMPOUND INTEREST. 

CONTENTS. 

Definition—Example. What amount will accrue after five years by investing 
a capital of $100 @3% per annum compound interest? The four fundamental 
operations of the calculation of compound interest—First Example. Find the 
accrued amount—Second Example. Find the capital—Third Example. Find 
the rate of compound interest—Fourth Example. Find the period of time— 
Compound Interest computed semi-annually, quarterly and monthly—Example. 
Computation of compound interest semi-annually, quarterly and monthly—Solu¬ 
tion by the Tables. 

— o — o — o — o — 

COMPOUND Interest 


A capital is invested at compound interest when the interest that accrues^ 
is added to the capital at the end of each year or other period, and is computed 
on the whole as a new capital. 

Example—^W hat amount will accrue after 5 years by investing a capital 
of $100 @ 3% per annum compound interest? 

The following is the long way, arithmetical solution of the example:— 


$100 

3% 

3.00 

100 

$103 

3% 

3.09 

103 

$106.09 

3 % 

3.1827 

106.09 

$109.2727 

3% 

3.278181 

109.2727 

$112.550881 

3% 

3.37652643 

112.550881 

$115.92740743 


Capital 

Interest on the capital for the 1st year 
Add Capital 

Capital at end of 1st year 

Interest on the capital for the 2nd year 
Add Capital 

Capital at end of 2nd year 

Interest on the capital for the 3rd year 
Add Capital 

Capital at end of 3rd year 

Interest on capital for the 4th year 
Add Capital 

Capital at end of 4th year 

Interest on capital for the 5th year 
Add Capital 

Capital at end of 5th year 


1 














ANNUITIES AND AMORTIZATION TABLES 


Thus the $100 capital becomes $115.9274 after 5 years at 3% compound 
interest. 

NOTE.—This arithmetical solution changed to the algebraic equation 
in which the elements are as follows, produces the same result by a 
much simpler method. 

5=the accrued amount, in this case $115.9274. 

c=the Capital, in this case $100. 

q=the unit, $1, plus its interest, in this case 1.03. 

n=the period of years, in this case 5. 

By the algebraic equation of S=ccp, 115.9274=100X1.03^ 

By the tables 1.03^=1.159274; thus 1.159274X100=$! 15.9274, as above. 

— o — o — o — o- 

THE FOUR FUNDAMENTAL OPERATIONS OF COMPOUND INTEREST. 

FIRST EXAMPLE, S=Cq^ 

What amount will a capital of $14523 become after 25 years by investing it 
@4% per annum compound interest? Table I, page 26, shows that $1 
invested at 4% compound interest will become 2.665830 after 25 years; there¬ 
fore $14523 will become: 

2.665830 X 14523=$38715.85. 

SECOND EXAMPLE, C=-^ 

q 

What capital must be invested @ 3%% per annum compound interest to 
obtain $50000 after 25 years ? 

Table I, page 26, shows that $1. after 25 years @ 3%% per annum 
-compound interest will become $2.510166; therefore the calculation by propor¬ 
tion will read: 

2.510166 : 1=50000 : a: 

50000^2.510166=$19919. 

But, as explained in the Preface, the algebraic equation of S=cq^ has four 
elements, and consequently there are four problems, in each of which one element 
is unknown. 

In this case the unknown element is the capital C, and the problem is solved 

by the equation C=-^; but as division is more difficult than multiplication, 

q 

table V was made, which gives the unknown capital or actual value C, of an ac¬ 
crued amount 5, divided by the unit plus its interest Q, for a period of time N, 
and by only a simple multiplication any unknown capital or actual value is deter¬ 
mined, thus: 

Table V, page 166, shows that the actual value of $1. at compound discount 
of 3%%, for 25 years, is 0.3983801; thus the actual value of $50,000 will be: 

0.3983801 X50000=$19919.005, 

the same result as was obtained by the method shown above, but by a much 
easier one. 

NOTE:—The next chapter is devoted to these calculations of compound 
discount. 


2 



ANNUITIES AND AMORTIZATION TABLES 


Third example, Q^yj 

(а) At what rate of compound interest must a capital of $5000 be in¬ 
vested to become $14626.30 in 22 years ? 

If $5000 becomes $14626.30 in 22 years, $1. will become: 

14626.30-^5000=2.92526. 

To find the rate of compound interest, follow the 22nd year line of Table I to 
the number 2.92526, which is in the column of 5% per annum. 

(б) At what rate of compound interest must a capital of $5000 be in¬ 
vested to become $17500 in 22 years? 

If $5000 becomes $17500 in 22 years, $1. will become: 

17500-^-5000=3.5 

Following the 22nd year line of the Table I to the number 3.421124, we find it 
corresponds to 5%%; and the next nearest number 3.511193 corresponds to 
578% ; consequently the rate of compound interest is a rate between 5%% and 
578% per annum. To fix the exact rate, the reasoning will be as follows: The 
difference between 3.511193 and 3.421124 is 0.090069, which represents, as 
above, an increase in the rate of interest of 78 of 1% or 0.125%. Therefore 
what is the increase in the rate for the difference between 3.5 and 3.421124 
which is 0.078876? 

The calculation by proportion will read: 

0.090069 : 0.125=0.078876 : x; or x=0.125X0.078876-^-0.090069=0.1095; 
consequently 5% or 5.75%-(-0.1095% =5.8595% the exact rate of compound 
interest. By logarithms the result would be 5.8596%, 

FOURTH EXAMPLE, N=- ^°SS 

log q 

In now many years will a capital of $15000, invested @4% per annum 
compound interest, become $35000? 

If $15000 becomes $35000 @ 4%, $1. will become: 

35000-^-15000=2.333 

In the column 4% of Table I, the two nearest numbers are 2.278764 in 
the line of 21 years, and 2.369914 in the line of 22 years; consequently the 
answer is between 21 and 22 years. To find the exact period of time the 
reasoning will be as follows: 

The difference between 2.278764 and 2.369914 is 0.09015, which rep¬ 
resents, as above, one year. Therefore, what period of time is represented 
by the difference between 2.333 . . . and 2.278764, which is 0.054569 ? By pro¬ 
portion 0.09015 : 1=0.054569 : x; or x=lX0.054569-^-0.09015=0.6053 of a 
year. This decimal part of a year represents 7 months and 8 days. By loga¬ 
rithms the result is 21 years, 7 months and 7 days. 

In the foregoing pages the plan of compounding the interest has been on 
the basis of annual periods, but in practice it is more frequently compounded 


3 





ANNUITIES AND AMORTIZATION TABLES 


semi-annually, and often quarterly. In an investment or loan where the inter¬ 
est is payable semi-annually or quarterly, the rate of interest and the period of 
time must be fixed accordingly, i.e., instead of calculating the interest 
e.g. @4% per annum, if it is payable semi-annually or quarterly, the calcula¬ 
tion must be made @ 2% for semi-annual periods, or @ 1% for quarterly 
periods respectively. Consequently the algebraic equations used in this chap¬ 
ter apply also when the interest is compounded semi-annually, quarterly,, 
monthly, weekly or daily. But it must be noted that the net result of an 
annual rate will not be equal to twice that of a semi-annual rate, or four times 
a quarterly rate. This is demonstrated by the following practical example. 

Example—A Savings Bank received on the same date $4000 from four 
different depositors, i.e., $1000 from each, and agreed to pay 6% per annum 
for 10 years, A's interest to be compounded annually, B's semi-annually, Cs 
quarterly and D’s monthly. 


o — o — o — o — 


SOLUTION By The tables 


A invested $1000 for 10 yearly periods @ 6% compound interest per an¬ 
num. Table I, page 42, shows that $1. @ 6% for 10 periods becomes 1.790849; 
therefore $1000 will become: 1.790849X1000=$1790.849. 

B invested $1000 for 20 semi-annual periods @3% compound interest per 
period of six months. Table I, page 18, shows that $1. @ 3% for 20 periods 
becomes 1.806109; therefore $1000 will become: 1.806109X1000=$1806.109. 

C invested $1000 for forty quarterly periods @ 1 V 2 % compound interest 
per period of three months. Table I, page 7, shows that $1. @ iy 2 % for 40 
periods becomes 1.814011; therefore $1000 will become: 


1.814011 X1000=$1814.011. 


D invested $1000 for 120 periods @ y 2 % compound interest per month. 
Table I, page 5, shows that $1. @ ¥ 2 % for 100 periods becomes 1.646683, and 
by the same table, page 2, @ ¥ 2 % for 20 periods it becomes 1.104897; there¬ 
fore for 120 periods it will become: 1.646683X1.104897=1.819415106591; 
therefore $1000 will become 1.819415106591 X1000=$1819.415. By tables 
extended up to 500 years, and by logarithms, the result for 120 periods for 
$1000 @ %% per period would be $1819.415. 

Consequently, A after 10 years will receive $1790.849 



1806.109 

1814.011 

1819.415 


notwithstanding that there was the same annual rate of interest and the same 
period of time, the different net results eventuating solely from the different, 
bases of the compounding of the interest. 


4 




ANNUITIES AND AMORTIZATION TABLES 


CHAPTER 11 


COMPOUND DISCOUNT 
CONTENTS 

Definition—Problem. What is the actual value or the capital C, which will 
have increased after N years to an amount S at compound interest ?—First 
Example. Find the actual value of an amount.—Problem. What is the actual 
value or the capital C, which will have increased after N years, at compound 
interest, to an amount S payable by instalments ?—Second Example. Find 
the actual value of an amount payable by instalments—Tabular illustration— 
Problem. What is the actual value or the capital C upon which an annuity A is 
received every year for a period of years N at compound discount ?—Third ex¬ 
ample. Find the actual value of an annuity—Fourth example. Find the 
actual value of a semi-annuity—^Remark. Comparison of semi-annuities with 
annuities. 

-o-O-0 — 0- 


COMPOUND DISCOUNT 

Compound discount is the method used to determine the actual value or 
the capital of an amount, which, if it were placed at compound interest, would 
have amounted to a certain sum, f.e., an original capital C would have 
amounted by compound interest to an accumulated amount S after a term 
of N years. Compound Discount determines the actual value or the capital C 
of the accumulated amount S at any desired time within the foreshortened 
period N. This is also known in finance as present value. 

The equation of compound interest is S=cq'^; therefore, the equation of com¬ 


pound discount will be 



This is identical to No. 2 of the Preface, and problems of this chapter 
may be solved by Table I, but more readily by Table V, which is the outcome 
of this form of equation. 

-_0 -O — 0 — 0 — 


SOLUTION BY THE TABLES 
PROBLEM 

What is the actual value or the capital C, which will have increased after 
N years to an amount S at compound interest ? 

FIRST EXAMPLE 

A father bequeathed to his son a fund invested with a Trust company, pay¬ 
able on the son’s attaining the age of 21 years, or 15 years after the date of the 
father’s death, which will then amount to $1,000,000; but the son also died, and 
the mother who inherits this amount desires to discount it today @4% com¬ 
pound discount. What is the actual value of the $1,000,000 payable after 15 
years; or what amount shall be paid tp the mother today? 

5 





ANNUITIES AND AMORTIZATION TABLES 


Table I, page 26, shows that $1. after 15 years @ 4% compound inter¬ 
est will become $1.800941. Therefore, the actual value or the capital of an 
amount of $1.800941, payable after 15 years @4% compound discount, is $1 
today. 

The example stated in the form of a proportion will read: 

1.800941 : 1 = 1,000,000 : a: ; hence, a: = $555,265.27 
Also Table V, page 170, shows that the actual value of $1. payable after 15 
years @4% compound discount is 0.5552654; therefore the actual value of 
$1,000,000 will be, 0.5552654 Xl,000,000=$555,265.40. The result is prac¬ 
tically the same having been reached through Table I or Table V. 

_0—o—o- 

PROBLEM 

What is the actual value or the capital C, which will have increased 
after different periods of years N, at compound interest, to an amount 5, payable 
by instalments? 

SECOND EXAMPLE 

A large building is sold for an amount to be paid as follows: $2,000,000 
cash, $3,000,000 after 5 years, $4,000,000 after 10 years, and $1,000,000 after 
15 years; total, $10,000,000. The purchaser having an unexpected surplus of 
cash in hand wishes, however, to change the terms of the payment and to pay 
the whole price of the building @ 4^4% compound discount. What is the 
actual value of the property, or what is the total amount that shall be paid ? 

For the first payment of $2,000,000 cash there is no calculation to be made. 
For the second payment of $3,000,000 to be paid after 5 years, the solution will be 
as follows: The actual value of $1. payable after 5 years at 4^4% compound 
discount is, according to Table V, page 170, 0.8121188; therefore the actual 
value of $3,000,000 will be: 0.8121188X3,000,000=$2,436,356.40. 

For the third payment of $4,000,000 the solution is: The actual value of 
$1. payable after 10 years @ 4^4% compound discount is, according to 
Table V, page 170, 0.6595366; therefore the actual value of $4,000,000 will, be: 

0.6595366 X 4,000,000=$2,638,146.40. 

For the fourth payment of $1,000,000 the solution is: The actual value 
of $1. payable after 15 years @ 4^4% compound discount is, according to 
Table V, page 170, 0.5356220; therefore the actual value of $1,000,000 will be: 

0.5356220 X 1,000,000=$535622.00 
Therefore the actual value of the property will be: 

1st payment Cash $2,000,000.00 Cash $2,000,000 


2nd 

“ “ 2,436,356.40 instead of 

3,000,000 after 

5 years 

3rd 

“ “ 2,638,146.40 “ 

4,000,000 “ 

10 “ 

4th 

“ “ 535,622.00 “ 

1,000,000 “ 

15 “ 


Total Cash $7,610,124.80 “ 

$10,000,000 by instalments 


6 











ANNUITIES AND AMORTIZATION TABLES 


PROBLEM 

What is the actual value or the capital C, upon which an annuity A will 
be received every year for a period of years N at compound discount ? 

Third example 

A man bequeathed to his son in trust an annuity of $20,000, payable 
every year for 24 years, but the son desires to discount it today @3% com¬ 
pound discount. What is the actual value of the annuity of $20,000, payable 
every year for 24 years @3% compound discount ; or what capital might be 
borrowed, which will be amortized by an annuity of $20,000 for 24 years @3% 
compound interest ? 

Table VI, page 200, shows that the actual value of an annuity of $1. 
payable every year for 24 years @3% compound discount, is 16.9355544; 
therefore the actual value of an annuity of $20,000 will be: 

16.9355544X20000=$338,711.088 

Also Table III, page 110, shows that to amortize a capital of $1. @ 3% 
in 24 years, the necessary annuity is 0.05904751. 

Therefore the actual value or the capital of an annuity of 0.05904751, 
payable for 24 years @ 3% compound interest, is $1. today; therefore the ex¬ 
ample stated in the form of a proportion will read: 

0.05904751 : 1^=20000 : x. Hence, a:=$ 338,710.30 
The result is practically the same having been reached through Table VI 
and Table III. 

— o — o — o- 

FOURTH EXAMPLE 

A man bequeathed to his son in trust a semi-annuity of $10,000 pay¬ 
able every six months for 24 years; but the son desires to discount it today 
@3% per annum compound discount. What is the actual value of this semi¬ 
annuity ; or what is the total amount that shall be paid to the son ? 

Table VII, page 231, shows that the actual value of a semi-annuity of $1* 
payable every six months for 24 years, or 48 semi-annuities of $1. @ 3% 
per annum compound discount, is 34.0426327; therefore the actual value of 
a semi-annuity of $10,000 will be 34.0426327 X 10000=$340,426.327. 

Remark —Attention is directed here to the fact that the actual value of 
two semr-annuities is not equal to the actual value of one annual annuity, even 
when there is the same annuity each year, the same rate of compound discount 
and the same length of time; e,g. in this example the actual value of 48 semi¬ 
annuities of $10,000 @3% per annum for 24 years is $340,426,327. The 
actual value of 24 annuities of $20,000 @ 3% for 24 years was found to be 
$338,711,088. The two aggregate results differ by $1,715,239, the only differ¬ 
ence in the two transactions being in the frequency of the periods at which the 
compound discount is reckoned, viz., semi-annual in one instance and annual in 
the other. 


7 




ANNUITIES AND AMORTIZATION TABLES 


CHAPTER III 

ANNUITIES 

CONTENTS 

Definition.—Annuities for Investment.—Problem. To invest the same 
amount of capital at the end of every year for a number of years at compound 
interest.—Problem. To invest the same amount of capital at the beginning of 
every year for a number of years at compound interest.—Example. Find the 
accumulated amount.—Note. Reasons for constructing Table II by making the 
investment at the end of every year, and the correlation which exists between 
the Tables.—Problem. Find the capital.—Problem. Find the rate of com¬ 
pound interest.—Problem. Find the period of time.—Note. Algebraic equa¬ 
tions solving the annuities and amortization problems.—Problem. What will 
be the accumulated amount after a number of years, when to a known capital 
a known annuity is added at the end of every year, at a known rate of compound 
interest ?—Example. Find the accumulated amount.—Problem. Find the out¬ 
standing amount of capital.—Problem. Find the capital when the annuity and 
outstanding amount of capital are known.—Problem. Find the annuity when 
the capital and the outstanding amount of capital are known.—Problem. Find 
the period of time.—Problem. Find the rate of compound interest.—Annuities 
for Instalment.—Amortization.—Definition.—Problem. Find the annuity.— 
Tabular Illustration.—Computation of amortization table.—Example.—Amor¬ 
tization of premiums.—Example. A Loan.—Problem. Find the capital.—Prob¬ 
lem. Find the period of time.—Problem. Find the rate of compound interest. 
—Semi-annual instalments.—Problem. Find the outstanding capital after 
payment of a number of annuities. 


— O-0 — 0 — 0—- 

Definition.—An annuity is the periodical payment of a fixed amount 
annually, or at more frequent, regular intervals, either for investment or 
amortization purposes. 

Annuities according to their function may be divided in two distinct 
classes; First: Annuities for Investment le. a periodical investment made 
annually, or at more frequent intervals, of a fixed amount, at a fixed rate of 
compound interest, and for a fixed period, for the purpose of saving and 
accumulating a capital; and Second: Annuities for Instalment, £. c. a peri¬ 
odical payment made annually, or at more frequent intervals, of a fixed 
amount, at a fixed rate of compound interest, either for a fixed period for 
the purpose of amortizing or extinguishing a debt, or in perpetuity; those 
of the latter class comprising only government issues, like the British 
“Consols,” and the French “Rente Perpetuelle”, 


8 








ANNUITIES AND AMORTIZATION TABLES 


ANNUITIES FOR INVESTMENT OR SINKING FUNDS 

As stated in the preface, Table II is based upon the principle of the well 

known Geometric progression; and its equation is 5=-- *^^ -, in which the 
elements are,— 

a=The annuity, annual investment or annual income. 

< 7 =The value of $1 plus its interest for one year. 

n=The number of years or periods. 

5=The unknown or the accumulated amount. 

~ 0—>0 - 0 — 0 - 

PROBLEM 

To invest the same amount of capital at the end of every year for a num¬ 
ber of years at compound interest. 

Example—T o what amount will an annual investment of $1435. accum¬ 
ulate, if invested at the end of every year for thirty-five years, @ com¬ 

pound interest? 

Table II, page 77, shows that $1. invested at the end of every year for 35 
years @ 4%%, becomes $85.77813; therefore $1435 will become: 

85.77813X1435=$123,091.61655. 

-o-O-0 — 0 — 

PROBLEM 

To invest the same amount of capital at the beginning of every year for a 
number of years at compound interest. 

Example —To what amount will an annual investment of $1435, accumu¬ 
late, if invested at the beginning of every year for 35 years @ 4%% com¬ 
pound interest? 

Table II, page 77, shows that $1. invested at the end of every year for 36 
years @ 4%%, becomes $90.85263. 

Deduct from this amoun t $ 1.00 

Then $89.85263 is the amount which a yearly investment of 
$1. will become, if invested at the beginning of every year for 35 years @ 4%%. 
Therefore $1435. will become: 89.85263X1435=$128,938.524. 

— O-0-0-- 

Note —The reasons for constructing Table II by making the investment 
at the end of every year instead of the beginning are: First: The only invest¬ 
ment made at the beginning of every year is when a premium is paid upon 
Annuity Insurance, or a deposit of savings is made in a Savings Bank directly 
before a date when interest starts, or a payment is made at the beginning of 
each year or other agreed period of time, under an obligatory system of savings. 
Second: Because the income of any investment is naturally received by the 
investor at the end of the year or shorter period, and Third: Because of the 
correlation which exists between the three first tables, as demonstrated in this 
chapter, page 16. This correlation is also a manner of checking one table by 
the other two. 


2 


9 







ANNUITIES AND AMORTIZATION TABLES 


PROBLEM 

What amount must be invested at the end of every year to become after 
a known number of years, at a known rate of compound interest, the known 
accumulated amount? 

Example—W hat amount must be invested at the end of every year, to 
become after 30 years @ compound interest, an amount of $100,000? 

Table II, page 73, shows that $1. invested at the end of every year at 3%% 
for 30 years, becomes $53.7992. Thus the calculation by proportion will read: 
$53.7992:1=100,000: a:; or 100,000 h- 53.7992=$1858.7637, which is the amount 
of capital, which, if invested at the end of every year @ 3%% compound inter¬ 
est, will become after 30 years $100,000. 

— o — o — o — o — 

PROBLEM 

At what rate of compound interest must a fixed amount be invested at the 
end of every year, to become the known accumulated amount after a fixed 
number of years ? 

Solution—D ivide the larger known amount by the smaller one, and then 
find in Table II in the line of years, to what rate of interest this result cor¬ 
responds. 

Example.—A t what rate of compound interest has an annual investment 
of $6000 been invested at the end of every year, to become $180,000 after 
20 years? 

SOLUTION—180,000-5-6000=30. 

Table 11, page 76, line of 20 years shows that an annual investment of 
$1. at the end of every year accumulates to $29.77797 in 20 years @ 4%; and 
it accumlates to $30.56260 in 20 years ; therefore the unknown rate is 

between 4% and 4%%, and nearer 4%. If there is a necessity for more 
exactness the operation must be continued as in chapter I, page 3. 

— O—-O-O—'O — 

PROBLEM 

For how many years must a fixed amount be invested at the end of every 
year, to become the known accumulated amount, at a fixed rate of compound 
interest ? 

Solution—T he same as with the rate of interest Le. divide the larger 
known amount by the smaller one, and then find in Table II, column of rates of 
interest, to what number of years the result corresponds. 

Example—F or how many years has an annual investment of $1000 been 
invested at the end of every year, to become $60,000 @ 4y2% per annum? 

SOLUTION—60000^ 1000=60 

Table II, page 77, column of 4y2%, shows that an annual investment of 
$1. at the end of every year accumulates to $57.42307 in 29 years, and 
accumulates to $61.00709 in 30 years; therefore, the unknown number of years 
is between 29 and 30, and nearer 30. If there is a necessity for more 
exactness the operation must be continued as in chapter I, page 3. 

10 




ANNUITIES AND AMORTIZATION TABLES 


MARGINAL NOTE; 

Before continuing the demonstration and solution of the annuities problems by the Tables, it is advi. -ble to 
show the algebraic equations, which give the different solutions. 

It has been shown that to find the amount to which a capital will increase, invested at compound interest 
for a number of years, the equation is S=cq^. 

Also the equation of the amount to which an annual investment will accumulate, invested at compound in- 

c- aiq^ —1) 

terest for a number of years is ^— 

< 7—1 . 

Thus in case these two operations are made simultaneously, viz: To invest a capital at compound interest 
for a number of years, and to add to this an annual investment at the same compound interest and for the same 

period of time, the equation will be as follows: co” H- ^—z -. which is the addition of the above 

q —1 

two equations. But if, instead of adding an annual investment, an annuity or an annual instalment is 

^ „ a(<7"—1) 

deducted, the equation will read , 3 = cq — —- 


< 7—1 . 

c—1) 

In uniting these two equations the result will be, o— cq 31 —^ - - — 

q —1 . 


Thus the following equation will result dby4- 


(s cq^) {q —1) . . o . 

' ^ „ - -r^ -in which, by suppressing and 

< 7—1 


taking the positive sign, the result is the amortization equation which reads, A. - 


c<7” (<7—1) 


q —1. 

Keeping the same elements and their equivalents in case that C must be determined, the equation will read: 


^ « _ a(<7—1) ^ s _ a{q^ —1) 

Cq^—s-^—^—z -or C=—- TT 

q — 1 < 7 ^ q {q — 1 ) 


If TV must be determined: 


^ „ . a{q^ —1) 

5=c< 7”±—or cq 


^ 1) 

<3—1 


Replacing q^ by x, the equation will read 


cx. 


a(x-l) 


q —1 


s{q —1) 


c(< 7 —l)±;a 


Multiplied by q —1, it will read 

(c(<7—l)±;a) jc = s (<7—l)±a or 
Replacing x hy q^ and using the logarithms in each side, it will read 

P 

Replacing q —1 by the primitive form of and multiplying both numerator and denominator by lOO, 

the equation will read : , loQ spit 100 a 

^ O=log cp±'m~a 

los (sQitlOO a)—log (cpitlOO a) 

N=—^ --1- 

log q 

The value q can be obtained only by an equation of the power by algebra. 

These are the algebraic equations which solve the annuities and amortization problems. 


11 




















ANNUITIES AND AMORTIZATION TABLES 


PROBLEM 

What will be the accumulated amount after a number of years, when to a 
known capital a known annuity is added at the end of every year, at a known 
rate of compound interest ? 

a(q^—l) 


S = cq^ 


q—^ 


Example—W hat will be the accumulated amount, by investing a capital 
of $1000 for 25 years, @3% compound interest, and adding at the end of 
every year $120 at the same rate of compound interest. 

Table I, page 18, shows that $1. invested for 25 years @3% will become 
$2.093774; therefore c(7^==1000X 1.03^=1000 X2.093774=$2093.774. 

Table II, page 72, shows that $1. invested at the end of every year for 25 
years at 3% becomes $36.45913; 

therefore 


q —1 


=36.45913 X 120=$4375.0956 


consequently or 2093.774+4375.0956=$6468.870=S. 

— o — o — o — 

PROBLEM 

What amount will remain after a number of years, when from a known cap¬ 
ital, invested for a number of years at a fixed rate of compound interest, 
an annuity is paid at the end of every year? 

Example —Ist A man invested with a Trust Company $75,000 @414% 
per annum compound interest, and for 20 years received an annuity of $2400. 
per annum; and at the end of the 20th year he desired to know what amount 
then remained to his credit with the Trust Company. 

Table I, page 30, shows that $1. invested for 20 years, @ 414% compound 
interest becomes $2.29891; therefore c<7”=75000X2.29891=$172,418.25. 

Also Table II, page 76, shows that $1. invested every year for 20 years 
^ 414% compound interest, becomes $30.5626; 

— 1 ) 


therefore 


Consequently S=cq^- 


aU 


=2400 X 30.5626=$73350.24. 


q—1 


172418.25—73350.24=$99068.01 


2nd A Life insurance Company agrees to pay a client an annuity of $3650. 
per annum, payable quarterly, $912.50 each quarter, for 25 years, with the 
understanding that the client will invest with the company $57514.05 for 25 
years @4% per annum, the interest to be compounded quarterly. At the end 
of the 25th year the client desires to know how his account stands with the 
Insurance Company. 

Table II, page 67, shows that $1. invested every period for 100 quarterly 
periods, or 25 years, @1% per quarterly period, making 4% per annum, the 
interest being compounded quarterly, becomes $170.4830; 

12 











ANNUITIES AND AMORTIZATION TABLES 


therefore ^^^^ =912.5X 170.4830=$155,565.73 

Also Table I, page 5, shows that $ 1 . invested @ 4% per annum for 
25 years, the interest to be compounded quarterly, or 1 % per quarterly period 
for 100 periods, becomes 2.704830; 

therefore Ctf=57514.05 X2.704830=$155,565.73. 

Consequently S=c< 7 "—2^^^=155,565.73—155,565.73=0 

PROBLEM 

What capital has been invested, when a known annuity has been paid 
at the end of every year, at a fixed rate of compound interest, for a known 
number of years, and at the end of this period of time there is a known remain¬ 
ing amount? 

^ _s_ —1) 

< 7 " — 1 ) 

Example—T he City of New York issued a loan, and for the service of the 
loan (interest and amortization quota) the City paid annually $500,000 for 67 
years. At the end of this period the City was still owing $698,750, the rate of 
interest being 4%% per annum. What was the total amount borrowed ? 

Table II, page 78, shows that $1. invested every year for 67 years @ 
4%% per annum becomes $450.6025; 

therefore =$450.6025X500,000=$225,301,250. 

Adding to this the remaining amount of $698,750=$226,000,000; 

a(<7”—1) , ^ 

or -^T7j-+-5- 

Table I, page 36, shows that $1. invested @ 4%% per annum for 67 years 
becomes $22.40361; therefore to find the amount that New York City borrowed, 
the first amount should be divided by the second: 

226,000,000-^22.40361=$10,037,659.97. 

— o — o — o — o- 

PROBLEM 

What annuity has been paid yearly, when a known capital has been invested 
at a fixed rate of compound interest, for a known number of years, and at the 
end of this period of time there is a known amount remaining ? 

. Ksr—cq^) (q —1) 

q ^—1 

EXAMPLE— 1st An investor deposited with a Trust Company a capital of 
$300,000 for 15 years, at 4% per annum compound interest, the company 
agreeing to return $200,000 at the end of the 15th year, after having also paid 
to the investor a yearly annuity. What was the amount of the yearly annuity? 

Table I, page 26, shows that $1. invested @ 4% per annum for 15 years 
becomes $1.800941; therefore cq”=300,000 X 1.800941=$540,282.30. Deduct¬ 
ing from this amount 5, the amount to be returned $ 200 , 000 , there remains 
$340,282.30, which=a/^—5. 


13 










ANNUITIES AND AMORTIZATION TABLES 


Table II, page 76, shows that $1. invested every year @4% per annum 
for 15 years, becomes $20.02352; therefore the annuity, which will accumulate to 
$340,282.30 after 15 years at 4%, will be 340,282.30-^-20.02352=$16994.12. 

2nd A client deposited with an Insurance Company $30,000 for 15 years, 
at 4% per annum, compounded semi-annually; and the Company agreed at the 
end of the 15th year to return $20,000, also paying an annuity during this 
period in semi-annual payments. What was the amount of such semi-annuity? 

$1. invested for 15 years @ 4% per annum, compounded semi-annually, or 
2% for 30 semi-annual periods, becomes $1.811363; therefore, 

c< 7”=30000X 1.811363==$54,340.89. Deduct the amount to be returned 

20,000 

$34,340.89=c</"—5. 

To find the semi-annuity, which at the end of 15 years, @4% per annum, 
compounded semi-annually, will produce $34,340.89; divide this by 40.56815, 
which is the amount to which $1. will accumulate by a semi-annual investment, 
@2% per semi-annual period for 30 periods: 

34340.89-J-40.56815=$846.49 

PROBLEM 

For how many years must a known capital have been invested, at a 
known rate of compound interest, while a known annuity has been paid at the 
end of every year, and at the end of the unknown period a known amount has 
remained ? 

,, log {sp —100a)— logicp —100a) 

log q 

EXAMPLE—A Trust Company agreed to pay to an investor an annuity of 
$16,994.12 on a capital of $300,000, @4% compound interest; and at the end 
of this unknown period of time the Company refunded to the investor $200,000. 
For how many years was this annuity paid to the investor? 

SOLUTION BY THE TABLES. 

This example can be solved only by trial and comparison of two or more cal¬ 
culations. In one the increased capital for a number of years must be deter¬ 
mined ; and in the other the accumulated annuity for the same period. The 
difference between the accumulated annuity and the increased capital must be 
equal to the remaining amount. A trial will be made for the 10th year as 
follows: 

Table I, page 26, shows that $1. invested @4% per annum, compound 
interest for 10 years becomes $1.480243; therefore $300,000 will become: 

300,000 X 1.480243=$444,072.90. 

Also Table II, page 76, shows that $1. invested at the end of cve/j? year 
for 10 years, @ 4% per annum compound interest, becomes $12.00607; there¬ 
fore, $16,994.12 will become $16,994.12 X12.00607=$204,032.60. The differ¬ 
ence between $204,032.60 and $444,072.90 is $240,040.30, which is considerably 
greater than the remaining amount of $200,000. Therefore, further trials 
must be made with other periods in the same way until the difference is equal 
to the remaining amount, as follows:— 


14 






ANNUITIES AND AMORTIZATION TABLES 


4% 1 

10 years 

11 years 

12 years 

13 years 

14 years 

Table I 






$300,000 
Capital 
Table II 

$444,072.90 

$461,835.60 

$480,309. 

$499,521.30 

$519,502.20 

$16,994.12 

- 204,032.60 

229,187.80 

255,349.40 

282,557.32 

310,853.90 

Annuity ' 

\ 

Difference 

$240,040.30 

$232,647.80 

$224,959.60 

$216,963.98 

$208,648.30 


15 years 






$540,282.30 






$340,282.10 






q—1 




Difference 

$200,000.20 





By these trials it is found that the period, during which the annuity was 
paid, according to the terms of the example, was 15 years. 

-o — o — o- 


PROBLEM 

At what rate of compound interest has a known capital been invested, 
for a known number of years, while a known annuity has been paid at the end 
of every year, and at the end of this period a known amount remains ? 

EXAMPLE—A city borrowed $10,087,660. For the service of the loan 
(interest and amortization quota) it paid annually $500,000 for 67 years; and at 
the end of this period the city still owed $698,750. At what rate of interest 
was the loan secured ? 

By these trials the rate is found to be 4%%. 

SOLUTION BY THE TABLES 

This example also can be solved only by trial and comparison of two or 
more calculations, as in the foregoing one. The increased capital at a trial 
rate of compound interest must be determined, and also the accumulated 
annuity at the same rate of compound interest. The difference between the 
two must be equal to the remaining amount, as in the previous example. 


67 Years 
Table I 
$10,087,660 
Capital 
Table II 
$500,000 
Annuity 

4^4% 


4%% 

$164,017,079.72 

• 179,519,750.00 

$192,567,176.05 

200,993,100.00 

$226,000,000.45=c</" 


Difference 

$15,502,670.28 

$8,425,924.95 

$698,750.45 


15 























ANNUITIES AND AMORTIZATION TABLES 


ANNUITIES FOR INSTALMENT AND AMORTIZATION 

Amortization : Is the extinction or doing to death, derived through the 
French from Latin— ad mortem —to death; a method of extinction of a debt. 
It was also the extinction of the rights in whole or part of the Feudal Seignory. 
According to the Roman tradition, which was maintained at the Frank epoch, 
the first charter of amortization was granted about the twelfth century, as 
shown in several contracts between Seignors and Churches, one of which men¬ 
tions its recent origin: “Cum ex modernorum uses, qui non permettunt Ecclesiae, 
ei largita sine admortizatione, tenere . . . (1159), and “ex nunc et in fu- 

turum admortizamus et admortizatum facimus . . . 

To amortize a debt, a loan, or a premium, is to extinguish it by partial, 
successive payments called annuities. To determine the amount of the annuities 
is to solve the calculations of the amortization quota, le. the proportion of the 
capital, which must be paid annually to amortize the original borrowed capital. 

The algebraic equation A = — is the basis of this calculation. The 

fundamental principle of the calcuation is the capitalization of the annuity 
every year during the continuance of the loan. 

When the solution is correct, the total amount of all the successive invest¬ 
ments, augmented by their compound interest for a period N, will be equal to 
the capital of the loan, plus its compound interest for the same period of time. 

Tables III and IV have been constructed after this mathematical principle 
on the basis of the algebraic equation mentioned above. 

They show the annuity which will amortize a capital of $1. for a number of 
periods at a fixed rate of interest. The annuity includes the interest and the 
amortization quota of the borrowed capital. 

EXAMPLE—Table III, page 117, shows that the annuity which will amor¬ 
tize a capital of $1. in 95 years @ is 0.04333093. According to the rule 
mentioned above, by capitalizing this annuity of $0.04333093 every year for 95 
years @ 4^4%, and adding all these successive investments together, they will 
equal the total of $1.00, invested @ 4^4% compound interest for this period of 
95 years. 

SOLUTION BY THE TABLES 

Table II shows that the accumulated amount of an annual investment of 
$1. for 95 years @ 4^4% is $1203.459; therefore, for an annual investment of 
0.04333093, it will be: 1203.459 X0.04333093=52.146997. 

Table I shows that $1. invested at the fixed rate of 4^4% compound interest 
for 95 years, becomes 52.14702; therefore, the first calculation is found to be 
correct. 

^ Furthermore, this example shows the relation which exists between the 
various tables of this work. 

PROBLEM 

Knowing the borrowed capital, the rate of compound interest and the 
period of time, find the annuity, f.e., the interest and the amortization quota. 
^ cq^{q—l) 


16 








ANNUITIES AND AMORTIZATION TABLES 


Example—A client borrows from a Trust Company $10,000 @4% per 
annum for 5 years, to be paid back in five equal annual instalments. 

Table III, page 114, shows that the annuity of $1. for 5 years @4% per 
annum is 0.2246279; therefore the annuity of $10,000 will be 
0.2246279 X 10,000=$2,246.279 
This annuity is divided for the first year as follows 
$ 400. Interest 

1,846.279 First year’s amortization quota of the capital 

$2,246.279 


This annuity, of course, will vary in detail each succeeding year, but will 
be the same in the aggregate each year. 


The computation of the entire amortization table of the debt is as follows: 


$10000 

1.04 

400.00 

10000 

10400.00 

2246.279 

8153.721 

1.04 

326.14884 
8153.721 
8479.86984 
2246.279 
6233.590 
_ 1.04 

249.34360 

6233.590 

6482.93360 

2246.279 

4236.654 
_1.04 

169.46616 

4236.654 

4406.120 

2246.279 

2159.841 

1.04 

86.39364 

2159.841 

2246.23464 

2246.279 


Capital 

Rate of interest 
First year’s interest 
Add Capital 

Total amount end of first year 
Less first year’s annuity 

Outstanding capital beginning of the second year 
Rate of interest 
Second year’s interest 
Add capital 

Total amount end of second year 

Less second year’s annuity 

Outstanding capital beginning of third year 

Rate of interest 

Third year’s interest 

Add capital 

Total amount end of third year 

Less third year’s annuity 

Outstanding capital beginning of fourth year 

Rate of interest 

Fourth year’s interest 

Add capital 

Total amount end of fourth year 

Less fourth year’s annuity 

Outstanding capital beginning of fifth year 

Rate of interest 

Fifth year’s interest 

Add capital 

Total amount end of fifth year 
Less fifth year’s annuity 


0.045 
























ANNUITIES AND AMORTIZATION TABLES 


With the aid of these figures, which show the exactitude of the solution, 
the following table shows for the end of every year the outstanding capital, the 
annuity, the interest and the amortization quota or portion of the capital paid 
every year to extinguish, at the end of 5 years, the whole debt: 


Years 

Outstanding 

Capital 


Interest 

Total 

A Remaining 

Annuity Amount 

1 

$10,000,000 

+ 

400. = 

10,400 

— 2,246.279 = 8,153.721 

2 

8,153.721 

+ 

326.148 = 

8,479.869 

— 2,246.279 = 6,233.590 

3 

6,233.590 

+ 

249.343 = 

6,482.933 

— 2,246.279 = 4,236.654 

4 

4,236.654 

+ 

169.466 = 

4,406.120 

— 2,246.279 = 2,159.841 

5 

2,159.841 

+ 

86.393 = 

2,246.234 

— 2,246.279 = 0. 


The annuity contains the interest and amortization quota, as follows: 


Years 

Annuity 

Interest 


Amortization quota 

1 

2,246.279 — 

400. 

= 

1,846.279 

2 

2,246.279 — 

326.148 

= 

1,920.131 

3 

2,246.279 — 

249.343 

= 

1,996.936 

4 

2,246.279 — 

169.466 

= 

2,076.813 

5 

2,246.279 — 

86.393 


2,159.886 

Total 

$11,231,395 = 

1,231.350 

+ 

$10,000,045 


—o—o—o—o— 

Example—A $1000 bond having 6 years to run, bearing interest at 5%, 
payable semi-annually, is purchased for $1,052.88 to net 4%. The premium of 
$52.88 must be amortized at the same rate of interest as the bond nets, and for 
the same period of time that the bond has to run. Consequently the maturity 
of the bond and the amortization of the premium will arrive at the same date. 
Thus the problem will be as follows: A premium of $52.88 @4% per annum, 
for 12 semi-annual periods, must be amortized, extinguished or paid back, in 
twelve equal semi-annual instalments or semi-annuities. 

Table IV, page 144, shows that the semi-annuity of $1. for 6 years or 12 
semi-annual periods, @4% per annum is 0.09455956; therefore the semi-annu¬ 
ity of $52.88 will be: 

0.09455956 X52.88=$5.000309 or $5. 

This semi-annuity of $5. is divided as follows for the first year. 

$1.0576 Interest 

3.9424 First year’s amortization quota of the premium 

$5.0000 Total annuity. This of course will vary in detail each suc¬ 
ceeding semi-annual period, but will be the same in the aggregate. 

In computing the amortization table as shown in the first example, the 
following table shows for the end of every semi-annual period the outstanding 
part of the premium, which added to the face value of the bond gives the book 
value of the bond; the interest on the premium added to the net interest on the 
bond, earned on the face value by the basis, gives the total interest earned on 
the basis at which the bond is bought; and the amortization quota or portion 
of the premium to be credited every six months to the purchase price of the 
bond, which will extinguish at the end of six years the whole premium. 

18 






ANNUITIES AND AMORTIZATION TABLES 


Semi¬ 

annual 

Periods 

Outstanding 
Premium at 
beginning of 
every period 


Interest 


Total 

Semi- 

Annuity 


Outstanding 
Premium at 
the end of 
every year 

Amorti¬ 

zation 

quota 

1 

52.88 

+ 

1.0576 

= 

53.9376 

— 5. 

= 

48.9376 

3.9424 

2 

48.9376 

+ 

0.9787 

= 

49.9163 

— 5. 

= 

44.9163 

4.0213 

3 

44.9163 

+ 

0.8983 

= 

45.8146 

— 5. 

= 

40.8146 

4.1017 

4 

40.8146 

+ 

0.8162 

= 

41.6308 

— 5. 

= 

36.6308 

4.1838 

5 

36.6308 

+ 

0.7326 

= 

37.3634 

— 5. 

= 

32.3634 

4.2674 

6 

32.3634 

+ 

0.6472 

== 

33.0106 

— 5. 

= 

28.0106 

4.3528 

7 

28.0106 

+ 

0.5602 

= 

28.5708 

— 5. 

= 

23.5708 

4.4398 

8 

23.5708 

+ 

0.4714 

= 

24.0422 

— 5. 

= 

19.0422 

4.5286 

9 

19.0422 

+ 

0.3808 

= 

19.4230 

— 5. 

= 

14.4230 

4.6192 

10 

14.4230 

+ 

0.2884 

= 

14.7114 

— 5. 

= 

9.7114 

4.7116 

11 

9.7114 

+ 

0.1942 

= 

9.9056 

— 5. 

= 

4.9056 

4.8058 

12 

4.9056 

+ 

0.0981 

== 

5.0037 

— 5. 

= 

0.0037 

4.9019 


Total 

7.1237 



60. 



52.8763 


Example —Suppose the United States Government issued a Liberty Loan 
for Democracy, representing a capital of thirty billion dollars 5% Gold Bonds, 
to be amortized by annual drawings in 75 years, the bonds being of a denomin¬ 
ation of $100. each. What annuity will the United States have to pay annually 
to amortize or extinguish this Liberty Loan in 75 years @5% interest? 

Table III, page 120, shows that the annuity, which will amortize a capital 
of $1. in 75 years @ 5% per annum, is 0.05132162; therefore for $30,000,000,000 
it will be: 

$30,000,000,000X0.05132162=$!,539,648,600, which will be divided for 
the first year thus: $1,500,000,000 Interest 

39,648,600 First year’s amortization quota 

$1,539,648,600 Total annuity. 

This of course will vary in detail each succeeding year, as may be seen from 
the following calculation of the second year’s annuity. 

The second year the loan is no longer thirty billions, because at the end 
of the first year there was paid through the amortization quota an amount of 
$39,648,600. 

$30,000,000,000—39,648,600=$29,960,351,400, the total amount of the 
loan outstanding at the end of the first year. 

The annuity of the second year will be divided thus: 

$1,498,017,570 Interest @ 5% on $29,960,351,400 
41,631,030 Second year’s amortization quota 

$1,539,648,600 Total annuity. 

NOTE— The annuity is the same in the aggregate each period, but varies 
in detail, always diminishing in the interest and increasing in the amortization 
quota. 

To compute the amortization table, showing for the end of every year, the 
outstanding capital, the annuity, the interest and amortization quota, the prox 
cess is practically the same as in the first example. 

19 













ANNUITIES AND AMORTIZATION TABLES 


Note—S ee also Chapter IV, Loans issued at par, and Chapter X, Farm 
Loans. 

Remark—F rom the foregoing it should be noticed that all the annuities 
and amortization problems are based on compound interest, which is added to 
the capital at the end of each period, producing a new interest. 

-0—0—o—o- 

PROBLEM 

Knowing the annuity or the necessary amount to amortize a borrowed 
capital, the rate of interest and the period of time, find the capital that may be 
borrowed. 

^ a(<7^—1) 

EXAMPLE—To make the example simple the same figures will be used as 
in the first example. 

What capital may a man borrow, when he is able to use $2246.279 of his 
income as an annuity for 5 years @4% per annum? 

Table III, page 114, shows that to amortize a capital of $1. @ 4% in 5 years, 
the necessary annuity is 0.2246279. Therefore with an annuity of $2246.279 
the capital which may be amortized will be: 

2246.279-^0.2246279, which=$10000. 

This problem also may be solved more easily by Table VI. 

Table VI, page 204, shows that the actual value of an annuity of $1. for 5 
years @ 4^^?, is 4.4518236. Therefore the actual value of an annuity of 
$2246.279 will be 4.4518236 X2246.279=-10000.037. 

— o — o — o- 

PROBLEM 

Knowing the borrowed capital, the annuity and the rate of interest, find 
the period of time. 

^r_ loS a—los [g—c(f7—1)] 

log q 

EXAMPLE—The same figures as in the first example will be used. 

For how many years must a man pay an annuity of $2246.279 to amortize 
a capital of $10,000 @ 4 % interest? 

First the annuity of $1. must be determined, as follows: 

The annuity of $10000 being $2246.279 the annuity of $1. will be 0.2246279 

Table III, page 114, shows that the annuity of $1. @ 4% is $0.2246279 in 
the line of 5 years, which is the period in consideration. 

In practice this exactness does not always follow. Therefore the following 
example is added. 

For how many years must a man pay an annuity of $300. to amortize a 
a capital of $4000. @5% Interest? 

The annuity of $4000 being 300., the annuity of $1. will be 300-^-4000= 
$0,075. Table III, page 118, column 5% shows that for 22 years the annuity is 
0.07597052; and for 23 years the annuity is 0.07413683. Consequently the 
period is between 22 and 23 years. 


20 






ANTUITIES AND AMORTIZATION TABLES 


To bring this result to a point of exactness the calculation may be contin¬ 
ued as follows: 

The difference between the two annuites of 0.07597052 and 0.075 being 
0.00097052, the reasoning will be as follows: 

When the annuity diminishes by 0.00183369 the time increases by one 
year; therefore 'when the annuity diminishes by 0.00097052 the time increases 
by 1X0.00097052^0.00183369=0.529, which represents six months and ten 
days, i.e. 22 years, six months, ten days. 

—o—o—o— 

PROBLEM 

Knowing the borrowed capital, the annuity and the period of time, find 
the rate of interest. 

_a — 1 ) 

c (f —1 

Example —At what rate of interest may a man boiTOw $10,000, paying an 
annuity of $2246.279 for 5 years to amortize his debt? 

Solution—F irst must be found the annuity of $1. The annuity of $10,000 
being 2246.279, the annuity of $1. is 0.2246279. Table III, page 114, line of 5 
years shows the annuity for $1. as 0.2246279, corresponding to a rate of 4% 
per annum. 

If the rate of interest cannot be found exactly with the tables, then a pro¬ 
cedure similar to that of determining the length of time must be used, as in the 
foregoing example. 

PROBLEM 

Knowing the borrowed capital, the annuity, the length of time and the rate 
of interest, find the amount of the remaining capital due after a payment of a 
number of annuities. 

SOLUTION A —Divide the annuity of the loan by the annuity of $1. for the 
remaining leijgth of time. 

To find the remaining capital after a payment of 3 annuites of $2246.279 
each, the loan being made for five years @ 4% on $10,000 capital. 

The annuity of the loan is $2246.279. 

The annuity of $1. for the remaining two years is 0.5301960, found in Table 
III, page 114, column 4%, line 2 years; 

therefore, 2246.279-^0.5301960=$4236.69, 
w^hich is the amount computed in the amortization table of the loan on page 18. 

SOLUTION B —This problem may also be solved more easily by Table VI. 
Page 204, shows that the actual value of an annuity of $1. for two years @4% 
is 1.8860946; therefore the actual value of an annuity of $2246.279 wdll be 
1.8860946 X 2246.279=$4236.6946. 

SEMI-ANNUAL INSTALMENT 

The above examples have been solved on the basis that the annuity is paid 
yearly, at the end of each year; but in practice very often, as the Farm Loan 
Act also permits, the annuity is payable in semi-annual instalments. Therefore 
the examples must be solved by Tables IV and VII, instead of Tables III 
and VI. “ See also Farm Loans. Chapter X.” 

21 





ANNUITIES AND AMORTIZATION TABLES 


CHAPTER IV 
LOANS ISSUED AT PAR 
CONTENTS 

Definition—Securities—Rate of issue—Nominal rate—Example—The 
City of New York issues 100,000 bonds or obligations of $1000 each, bearing 
a $40 interest coupon per annum, the loan to be amortized in 10 years by ten 
equal annual instalments.—Find the borrowed capital—Find the annuity—Find 
the amortization quota of bonds—Tabular illustration of amortization— Liberty 
Loan—Tabular illustration of the Liberty Loan. 

— o — o — o- 

Definition—A loan is a transaction, in which money is lent to a borrower, 
and for which he pays interest, while he has the use of it. Such a transaction 
may be arranged by an individual, corporation, town, state or government. 
There must always be two parties to a loan; 1st, the party who lends the money, 
the lender; and 2nd, the party who borrows, the borrower. The lender in ex¬ 
change for his money receives for security a bond or other document of value 
signed by the borrower. 

There are many kinds of securities: bonds and income certificates of 
governments, and stocks and bonds of corporations and municipalities. Their 
duration is fixed, when the securities are to be redeemed at a specified date of 
maturity or amortized by successive, partial payments; or their duration is not 
fixed, as e.g. in income certificates, which are perpetual, and only the income is 
paid by the government, which does not pledge the redemption of the principal. 
Stocks represent a part of the capital, issued by corporations, and their income 
varies with the earnings of the corporation. 

The price at which a bond is sold is called the rate of issue or market price. 
The face value of a bond, or the price at which it will be redeemed, is called the 
nominal rate or the redemption price. 

The law of supply and demand and the credit of the borrower always deter¬ 
mine the rate of issue and the redemption price, which may be different from the 
face value of a bond. 

The foregoing chapters have treated of the class of loans where the bor¬ 
rowed capital and the redeemed capital are the same, and where the borrower must 
provide for the payment of not only the agreed interest of the loan, but also for 
the redemption of the borrowed capital by successive partial payments 
called the amortization quotas. The following example will explain the 
practical operation of the amortization quota of a loan. 

EXAMPLE—The City of New York issues 100,000 bonds @ $1000 each, 
bearing a $40 interest coupon per annum, the loan to be amortized in 10 years, 
by 10 equal annual instalments. 


22 



ANNUITIES AND AMORTIZATION TABLES 


The entire borrowed capital is in this case 100,000 X$1000=$100,000,000. 
The annuity payable every year to amortize the loan in 10 years @4% equals 
the annuity of $1. @ 4% for 10 years, which is 0.1232910 as per Table III, 
page 114, multiplied by the capital, thus 0.1232910 X 100,000,000=$12,329,100, 
which for the first year will be divided as follows: 

For the interest @4% per annum $4,000,000 

For the amortization quota of the capital 8,329,100 

Total annuity $12,329,100 

Thus from the total annuity, $4,000,000 have been employed for the pay¬ 
ment of the interest, and $8,329,100 for the redemption of ^329 bonds @ $1000 
each, plus a fraction of 0.100 of a bond. 

Note—T he fractional part of a bond must always be considered in the 
calculations. 

The second year 8329 bonds must first be redeemed, and then the 
interest on 8329 bonds, which have been redeemed the previous year. In this 
case they represent, at the rate of $40 per bond on 8329 bonds, $333,160 of 
interest. To this amount add the interest on the fraction 0.100 of a bond, $4. 
This will give $333,160+4+100=$333,264, which will redeem 333 bonds @ 
$1000 each, with 0.264 of a bond carried forward. Thus the second year there 
will be redeemed 8329+333=8662 bonds. 

In continuing these calculations for the following years, the number of bonds 
amortized increases every year; and at the end of the 10th year the total obli¬ 
gation of 100,000 bonds is redeemed. 

But this procedure to determine the number of bonds to be redeemed every 
year is very laborious, therefore the following procedure must be used. 

Knowing the first year’s amortization quota, multiply it successively for 
every year by the unit plus its interest for a year, and divide each product by 
the redemption price of the bonds; or, knowing the number of bonds to be 
redeemed at the end of the first year, multiply this number successively for 
every year by the unit plus its interest for a year, i.e. 


(a) $8,329,100 

1.04 

33,316,400 

8,329,100 

$866,226,400 

8662.264 


first year’s amortization quota 
multiply by the unit plus its interest 


divide by the redemption price of $1000 
bonds to be redeemed the second year 

or 


(i) 8329.10 bonds to be redeemed the first year 

1,04 multiply by the unit plus its interest 

3,331,640 

832,910 

8662.264 bonds to be redeemed the second year 


23 
















ANNUITIES AND AMORTIZATION TABLES 


In continuing these operations up to the 10th year the following Tabular 


Illustration of amortization will be made. 



Years 

Outstanding Capital 

Interest 

Amorttotion Quota 

1 

$100,000,000 

$4,000,000 

$ 8,329,100 

8,329 

2 

91,670,900 

3,666,836 

8,662,264 

8,662 

3 

83,008,636 

3,320,345 

9,008,755 

9,009 

4 

73,999,881 

2,959,995 

9,369,105 

9,369 

5 

64,630,776 

2,585,231 

9,743,869 

9,744 

6 

54,886,907 

2,195,476 

10,133,624 

10,134 

7 

44,753,283 

1,790,131 

10,538,969 

10,539 

8 

34,214,314 

1,368,572 

10,960,528 

10,960 

9 

23,253,786 

930,151 

11,398,949 

11,399 

10 

11,854,837 

474,193 

11,854,907 

11,855 



$23,290,930 

$100,000,070 

100,000 


Total $123,291,000 


It is seen from the Tabular Illustration of amortization that the grand 
total of the amortization quotas shows an excess of 70 units over the capital. 
This difference is very small compared with the total and is inevitable although 
seven decimal places are used. 

An easy method to check the multiplications while in progress, especially if 
there is a long period of years and if the amounts are very large, is to verify 
the operations by Table I, by multiplying for any year the first year’s amortiza¬ 
tion quota by the corresponding number of the table, i.e. for the above example 
verify the amortization quota of the 8th year thus: 

Table I, page 26, 4% interest, the 7th year shows the value of the unit 
to be 1.31593; therefore for the $8,329,100, which is the first year’s amortiz¬ 
ation quota it will be: $8,329,100X1.31593=10,960,512, with a difference of 
only 16 units. This difference is due to using only seven decimal figures. 

— o-O-O-O—" 

LOAN 

UNITED STATES OF AMERICA 
Liberty Loan for Democracy 

Capital $30,000,000,000. 5% Gold Bonds. 

To be amortized by annual drawings in 75 years. Interest payable 

annually. 

Class of bonds: Coupon bonds. 

Denomination: $100 each, and numbered from 000,000,001 to 300,000,000. 

Redemption: On December 1st of every year a drawing will take place 
in the Treasury Department, where a number of bonds will be drawn representing 
at par an amount equal to the annual amortization quota of the loan. The num¬ 
bers drawn will be called in at par on December 10th of each year. 

24 









ANNUITIES AND AMORTIZATION TABLES 


The annuity of the loan will be: 

$30,000,000,000X0.05132162=$!,539,648,600. 
The chart of the loan is as follows:— 


TToara. 

Outstanding 
bonds at the 

Annual 

Annual 

Amortization 

Outstanding 
bonds at 


beginning of 

Interest charges 

quota. Number 

the end of 


every year. 

Oa vXXC/ 

of bonds. 

every year. 

1 

300,000,000 

$1,500,000,000 

396,486 

299,603,514 

2 

299,603,514 

1,498,017,570 

416,310 

299,187,204 

3 

299,187,204 

1,495,936,020 

437,126 

298,750,078 

4 

298,750,078 

1,493,750,391 

458,982 

298,291,096 

5 

298,291,096 

1,491,455,481 

481,931 

297,809,165 

6 

297,809,165 

1,489,045,825 

506,028 

297,303,137 

7 

297,303,137 

1,486,515,685 

531,329 

296,771,808 

8 

296,771,808 

1,483,859,040 

557,896 

296,213,912 

9 

296,213,912 

1,481,069,560 

585,790 

295,628,122 

10 . 

295,628,122 

1,478,140,610 

615,080 

295,013,042 

11 

295,013,042 

1,475,065,210 

645,834 

294,367,208 

12 

294,367,208 

1,471,836,040 

678,126 

293,689,082 

13 

293,689,082 

1,468,445,412 

712,032 

292,977,050 

14 

292,977,050 

1,464,885,253 

747,633 

292,229,417 

15 

292,229,417 

1,461,147,085 

785,015 

291,444,402 

16 

291,444,402 

1,457,222,010 

834,266 

290,620,136 

17 

290,620,136 

1,453,100,680 

865,479 

289,754,657 

18 

289,754,657 

1,448,773,285 

908,753 

288,845,904 

19 

288,845,904 

1,444,229,520 

954,191 

287,891,713 

20 

287,891,713 

1,439,458,565 

1,001,900 

286,889,813 

61 

159,810,256 

799,051,280 

7,405,973 

152,404,283 

62 

' 152,404,283 

762,021,415 

7,776,272 

144,628,011 

63 

144,628,011 

723,140,055 

8,165,085 

136,462,926 

64 

136,462,926 

682,314,630 

8,573,340 

127,889,486 

65 

127,889,586 

639,447,930 

9,002,007 

118,887,579 

66 

118,887,579 

594,437,895 

9,452,107 

109,435,472 

67 

109,435,472 

547,177,360 

9,924,712 

99,510,760 

68 

99,510,760 

497,553,800 

10,420,948 

89,089,812 

69 

89,089,812* 

445,449,060 

10,941,996 

78,147,816 

70 

78,147,816 

390,739,080 

11,489,095 

66,658,721 

71 

66,658,721 

333,293,605 

12,063,550 

54,595,171 

72 

54,595,171 

272,975,855 

12,666,727 

41,928,444 

73 

41,928,444 

209,642,220 

13,300,064 

28,628,380 

74 

28,628,380 

143,141,900 

13,965,067 

14,663,313 

75 

14,663,313 

73,316,565 

14,663,320 




$85,473,639,866 

300,000,051 



Grand Total $115,473,645,000 or 75 instalments of $1,539,648,600 each. 
3 25 








ANNUITIES AND AMORTIZATION TABLES 


CHAPTER V 

LOANS ISSUED AT A DIFFERENT RATE THAN PAR 
AND REDEEMED AT PAR 

CONTENTS 

Example.—Find the nominal capital.—Find the real capital.—Find the an¬ 
nuity.—Find the amortization quota of bonds.—Find the number of amortized 
bonds after a number of years.—Find when the half of the bonds issued have 
been amortized, or the probable date of the redemption of the bonds.—Capitaliza¬ 
tion rate.—Find the capitalization rate after payment of a number of annuities. 
—Real or effective rate of interest.—Tabular illustration of the railroad loan. 

example 

A railroad company having an income of $3,400,000 from its investments, 
decides to use this income for 75 years as an annuity on a loan, on the amortiza¬ 
tion plan, to raise funds for improvements, by issuing 100,000 bonds of a 
nominal and redemption value of $1000 each. The rate of issue, or the price 
at which the bonds are sold is $700 each, and each bond bears an interest 
coupon of $30 per annum. 

The following features of the issue are important both to the railroad com¬ 
pany and to the investors: 

/ st —What is the nominal capital of the loan ? 

100,000 bonds X $1000 nominal value=$100,000,000. 

2nd —What amount may the railroad company borrow ? 

100,000 bonds X $700 rate of issue=$70,000,000. 

3rd —What will be the annuity of the loan? 

Table III, page 112, column 3% for 75 years shows that the annuity of $1 
is: 0.03366798; therefore the annuity of $100,000,000 nominal value will be. 

0.03366798 X $100,000,000=$3,366,798. 
which will be divided as follows:— 

$3,000,000 interest at 3% 

366.798 amortization quota 

$3,366,798 total annuity, which will vary in detail each succeeding year, 
but will be the same in the aggregate each year. 

4th —What is the annual amortization quota of the bonds? 

{a) For the service of the first year’s amortization quota the 
amount is $366,798. 

Therefore $366,798-^$1000 par value=366.798 bonds. 

(NOTE.—In these calculations it is well to carry as many decimals 
as possible.) 

Thus 367 bonds are redeemed at the end of the first year, because 
the decimal 0.798 is more than one half. 


26 








ANNUITIES AND AMORTIZATION TABLES 


^ ^> ””””” .. “““ 

( h) For the second year $366,798 will be redeemed, and also the 
amount representing the interest on $366,798 at 3% thus: 

366,798 X 1.03=$377,802 

Therefore the number of bonds redeemed at the end of the second 
year will be: 377,802-^1000=377.80 bonds, or 378 bonds. 

The same result may be obtained thus:— 

367 bonds X 1.03=378.01 as above. 

(c) For the third year proceed in the same way as for the 
second, 

377,802X1.03=389,1.36-^-1000=389.136 bonds, or 
378X1.03=389.14 

Another method of solving the same example is:— 

^ Knowing the amount of the first year’s amortization quota, multiply it suc¬ 
cessively by the value of $1. at a fixed rate of compound interest for a number 
of years; see Table I, page 18, 3% compound interest. 

Multiply $366,798 by 1.03 for the 2nd year 

“ “ “ 1.0609 “ “ 3d “ 

“ “ “ 1.092727 “ “ 4th “ 

“ “ “ 1.125509 “ “ 5th 

and so on until the last year, and divide the amounts by 1000 the nominal value 
of the bonds, until the last year. 

It may be done also by multiplying the amortization quota of bonds of the 
first year successively by the value of $1. at a fixed rate of compound interest, 
as above. 

Multiply 366.798 bonds by 1.03 for the 2nd year 

u u a u ^ u u 3^ u 

“ “ 1.092727 “ “ 4th “ 

and so on until the last year. 

In compiling the following amortization table for this example, a simple 
method of solving two questions at the same time is shown. 

5th —How many bonds have been amortized after a number of years? 

Table II shows the value of $1. invested every year at a fixed rate of com¬ 
pound interest for a number of years. 

•Multiply the number in table II by the value of the first year’s amortiza¬ 
tion quota and divide by 1000, the nominal value of the bonds; or multiply the 
number of table II by the amount of bonds amortized the first year thus: 

How many bonds have been amortized after 42 years ? 

Table H, page 73, shows that $1. invested every year @ 3% compound 
interest for 42 years, accumulates to $82.0229; therefore: 

{a) 82.0229X$366,798=$30,085,836.67^1000=30,085.83 bonds. 

( b) 82.0229 X366.798 bonds=30,085.83 bonds. 

6th —How to determine when half of the bonds issued have been amortized, 
or what is the probable date of the redemption of the bonds, as it is designated 
in finance. 


27 




ANNUITIES AND AMORTIZATION TABLES 


When an annual amount of $366,798 amortizes @3% a capital of 
$50,000,000. (the half of the borrowed capital) after a number of years, an 
annual amount of $1. will amortize 50,000,000-^-366798=136. Table II, column 
3%, shows that $1. invested every year at 3% will take 55 years to produce 
$136 (table II, page 74, column 3%, for 55 years shows 136.0711). The prob¬ 
able date of the redemption of the bonds is about 55 years; at this period the 
number of the redeemed bonds is equal to the outstanding bonds. 

— o — o — o- 

CAPITALIZATION RATE 
7th —What is the capitalization rate ? 

The capitalization rate is the relation that the annuity, le. the interest plus 
the amortization quota, bears to the capital on the basis of an effective capital of 
$100. In the above example the annuity of $1. is 0.03366798; therefore the 
annuity of $100 is $3.366798, and 3.366798% would be the capitalization rate 
if the loan were issued at par; but the loan was sold at $700 per $1000 bond, 
or 70%; therefore 3.366798 X100=336.6798-^-70=4.81% the capitalization rate, 
or $3^66 per bond on a market price of $700. 

Conseqently the railroad company will redeem 4.81% per annum, including 
interest and amortization quotas on the amount borrowed for 75 years. 

This 4.81% is made up of 4.29% for the interest, at the rate of $3. for 
every $70, and 0.52% for the amortization quota. 

This calculation is correct only for the first year and must be modified sub¬ 
sequently as the bonds are redeemed. 

8th —What is the capitalization rate after payment of 25 annuities ? 

{a) When the market price is, as above, $700 per bond, how many 
bonds have been amortized at the end of 25 years must be found first, as in 
question 5. 

Table II, page 72, shows that $1. invested every year @3% compound 
interest for 25 years, accumulates to $36.45913 ; 
therefore 36.45913 X$366,798=$13,373,135-^-1000=13373.135 bonds. 
Thus there are 86,627 bonds outstanding, for which the railroad company 
will continue to pay the same annuity of $3,366,798, or for each bond 
$38,866 divided as follows:— 

$30.00 for interest coupon per bond. 

8.866 amortization quota. 

Thus the rate may be found by the following proportion. 

30 : 4.29=38.866 : at; or a:= 5.55% the capitalization rate. 

( h) When the market price is different, suppose $800 per bond, the 
temporary rate is 3.75%, and the following proportion will show the capi¬ 
talization rate:— 

30 : 3.75=38.866: x \ or x;=4.86% the capitalization rate. 

There is a simpler way to determine the capitalization rate by the Tables. 
First, find the annuity by Table III for a given length of time and interest; 
Second, multiply this annuity by 100. Third, multiply the result by the par 
value of the bonds, and Fourth, divide the product by the market value as 
follows: The duration of the loan will be for only fifty years more. Table III, 
page 111, shows that the annuity of a capital of $1. at 3% for a period of 50 

28 





ANNUITIES AND AMORTIZATION TABLES 


years, is $0.03886552; multiply this by 100 to make the rate 100%, and the 
product by $1000, the par value of the bond, and divide by $700, the market 
value, 

0.03886552 X 100=3.886552 X 1000=3,886.552-f-700=5.55 %. 

By making the same kind of calculation for a market price of $800, the capital¬ 
ization rate will be: 

0.03886552 X 100=3.886552 X 1000=3,886.552-f-800=4.86 % 

Thus the capitalization rate augments, when the amortization progresses,, 
and the chances for redemption are larger; on the other hand it diminishes, 
when the market price rises. 

-—0 — 0 — o- 

REAL RATE OP INTEREST 

The real or effective rate of interest of a loan is the real earning power 
rate of the real or effective capital, or the interest which must be paid in the 
annuity to amortize the real or effective capital. 

The easiest way to obtain the real rate of interest is through the capital¬ 
ization rate, as follows: The same example will be used as in the foregoing. 

It is seen there that the borrower pays an annuity of $3,366,798 for an 
effective capital of $70,000,000. 

If this annuity of $3,366,798 amortizes a real capital of $70,000,000, for 
amortizing a capital of $100. there will be needed an annuity of 

3,366,798X100-^70,000,000=4.809711; for $1. it will be 0.04809711. 
Table III, page 116, line of 75 years shows that this rate corresponds to the 
real rate of interest between 4%% and 4%%, because 0.04672104 is in the 
column of 414%, and 0.04900913 is in the column of 4%%. 

To bring this result to a point of exactness the calculation may be con¬ 
tinued by the calculation of proportion as follows: 

Subtracting the first from the second, the difference is 0.00228809; thus 
the reasoning will be, when the annuity augments by 0.00228809, the real in¬ 
terest augments from 414% to 4%% or 0.25%; therefore when the annuity 
augments from 0.04809711—0.04672104, or 0.00137607, the real interest will 
augment 0.00137607X0.25-^0.00228809=0.1503; adding 0.1503 to 4.50% the 
real interest is 4.6503%, at which the loan has been issued. 

This method of determining the real or effective rate of interest must be 
used also when the amortization has been in operation for any number of years. 
Determine first the capitalization rate, and then by table III, determine the real 
rate of interest which corresponds. 

The determination of the real rate of interest is exceedingly important 
because it is the basis of comparison between bonds, to find which is the most 
advantageous investment. 

The following table shows the outstanding number of bonds at the end of 
every year, the number of the redeemed bonds every year, the interest to be paid 
at the end of every year, the annual amortization quota, the capitalization rate 
at a market price of $700, the capitalization rate at a market price of $800, the 
real rate of interest at a market price of $700, and the real rate of interest at 
a market price of $800. 


29 



ANNUITIES AND AMORTIZATION TABLES 


TABLE OF AMORTIZATION 

Loan of $100,000,000 divided into 100,000 bonds of $1000 each redemption 
value, @3% per annum, to be redeemed in 75 years, on the amortization plan, 
the redeemed bonds to be determined by yearly drawings; the issue sold at $700 
per bond of $1000 par value. 

The ANNUITY of the loan is $3,366,798. 


Years 

Bonds to be 
Redeemed 

Redeemed 

Bonds 

Interest payable 
at the end of 
every year 

Yearly 

Amortization 

Capitalization Rate on 
a Market Price of 

$700 $800 

Real Rate of 
Interest on a 
Market Price of 
$700 $800 




$ 

$ 

% 

% 

% 

% 

1 

100,000 

367 

3,000,000 

366,798 

4.810 

4.208 

4.650 

3.983 

2 

99,633 

378 

2,988,996 

377,802 

4.827 

4.224 

4.661 

3.990 

3 

99,255 

389 

2,977,662 

389,136 

4.846 

4.240 

4.673 

3.997 

4 

98,866 

401 

2,965,988 

400,810 

4.865 

4.257 

4.685 

4.005 

5 

98,465 

413 

2,953,964 

412,834 

4.885 

4.274 

4.697 

4.012 

6 

98,052 

425 

2,941,579 

425,219 

4.905 

4.292 

4.709 

4.020 

7 

97,627 

438 

2,928,822 

437,976 

4.927 

4.311 

4.722 

4.028 

8 

97,189 

451 

2,915,683 

451,115 

4.949 

4.330 

4.736 

4.036 

9 

96,738 

464 

2,902,150 

464,648 

4.972 

4.350 

4.750 

4.044 

10 

96,274 

479 

2,888,211 

478,587 

4.996 

4.371 

4.764 

4.053 

11 

95,795 

493 

2,875,853 

492,945 

5.021 

4.393 

4.779 

4.062 

12 

95,302 

508 

2,859,065 

507,733 

5.047 

4.416 

4.795 

4.073 

13 

94,794 

523 

2,843,833 

522,965 

5.074 

4.439 

4.811 

4.082 

14 

94,271 

538 

2,828,144 

538,654 

5.102 

4.464 

4.827 

4.092 

15 

93,733 

555 

2,811,984 

554,814 

5.131 

4.490 

4.844 

4.103 

16 

93,178 

571 

2,795,340 

571,458 

5.162 

4.517 

4.862 

4.114 

17 

92,607 

589 

2,778,196 

588,602 

5.194 

4.544 

4.881 

4.125 

18 

92,018 

607 

2,760,538 

606,260 

5.227 

4.574 

4.901 

4.138 

19 

91,411 

624 

2,742,350 

624,448 

5.262 

4.604 

4.921 

4.150 

20 

90,787 

643 

2,723,617 

643,181 

5.298 

4.635 

4.942 

4.162 

21 

90,144 

663 

2,704,322 

662,476 

5.336 

4.669 

4.964 

4.176 

22 

89,481 

682 

2,684,448 

682,350 

5.375 

4.703 

4.987 

4.190 

23 

88,799 

703 

2,663,977 

702,821 

5.416 

4.739 

5.010 

4.204 

24 

88,096 

724 

2,642,892 

723,906 

5.459 

4.777 

5.034 

4.220 

25 

87,372 

746 

2,621,175 

745,623 

5.505 

4.817 

5.060 

4.236 

26 

86,626 

768 

2,598,806 

767,992 

5.552 

4.858 

5.087 

4.252 

27 

85,858 

791 

2,575,766 

791,032 

5.602 

4.902 

5.115 

4.269 

28 

85,067 

814 

2,552,035 

814,763 

5.654 

4.947 

5.145 

4.287 

29 

84,253 

839 

2,527,592 

839,206 

5.709 

4.995 

5.176 

4.306 

30 

83,414 

865 

2,502,416 

864,382 

5.766 

5.045 

5.208 

4.325 

31 

82,549 

890 

2,476,485 

890,313 

5.826 

5.098 

5.241 

4.346 

32 

81,659 

917 

2,449,775 

917,023 

5.890 

5.154 

5.277 

4.368 

33 

80,742 

945 

2,422,264 

944,534 

5.957 

5.212 

5.314 

4.390 

34 

79,797 

973 

2,393,928 

972,870 

6.027 

5.274 

5.353 

4.414 

35 

78,824 

1,002 

2,364,742 

1,002,056 

6.102 

5.339 

5.393 

4.439 


30 








ANNUITIES AND AMORTIZATION TABLES 


Years 

Bonds to be 
Redeemed 

Redeemed 

Bonds 

Interest payable 
at the end of 
every year 

Yearly 

Amortization 

Capitalization Rate on 
a Market Price of 

$700 $800 

Real Rate of 
Interest on a 
Market Price of 
$700 $800 

36 

77,872 

1,032 

2,334,680 

1,032,118 

6.180 

5.408 

5.436 

4.466 

37 

76,790 

1,063 

2,303,716 

1,063,082 

6.263 

5.480 

5.481 

4.493 

38 

75,727 

1,095 

2,271,824 

1,094,974 

6.351 

5.557 

5.529 

4.522 

39 

74,632 

1,128 

2,238,975 

1,127,823 

6.444 

5.639 

5.579 

4.553 

40 

73,504 

1,161 

2,205,140 

1,161,658 

6.543 

5.725 

5.632 

4.585 

41 

72,343 

1,197 

2,170,290 

1,196,508 

6.648 

5.817 

5.689 

4.619 

42 

71,146 

1,232 

2,134,395 

1,232,403 

6.760 

5.915 

5.750 

4.656 

43 

69,914 

1,269 

2,097,423 

1,269,375 

6.879 

6.019 

5.813 

4.694 

44 

68,645 

1,308 

2,059,342 

1,307,456 

7.007 

6.131 

5.881 

4.736 

45 

67,337 

1,347 

2,020,119 

1,346,679 

7.143 

6.250 

5.954 

4.780 

46 

65,990 

1,387 

1,979,718 

1,387,080 

7.228 

6.377 

6.030 

4.827 

47 

64,603 

1,428 

1,938,106 

1,428,692 

7.445 

6.514 

6.112 

4.876 

48 

63,175 

1,472 

1,895,245 

1,471,553 

7.613 

6.662 

6.200 

4.930 

49- 

61,703 

1,515 

1,851,099 

1,515,699 

7.795 

6.820 

6.295 

4.987 

50 

60,188 

1,561 

1,805,629 

1,561,169 

7.991 

6.992 

6.397 

5.049 

51 

58,627 

1,608 

l,'f58,794 

1,608,004 

8.204 

7.178 

6.508 

5.115 

52 

57,019 

1,656 

1,710,554 

1,656,244 

8.435 

7.381 

6.626 

5.188 

53 

55,363 

1,708 

1,660,867 

1,705,931 

8.688 

7.602 

6.757 

5.262 

54 

53,657 

1,757 

1,609,689 

1,757,109 

8.964 

7.843 

6.897 

5.352 

55 

51,900 

1,810 

1,556,976 

1,809,822 

9.267 

8.109 

7.051 

5.446 

56 

50,090 

1,864 

1,502,681 

1,864,117 

9.602 

8.402 

7.220 

5.543 

57 

48,226 

1,920 

1,446,757 

1,920,041 

9.973 

8.727 

7.407 

5.662 

58 

46,306 

1,978 

1,389,156 

1,977,642 

10.39 

9.089 

7.618 

5.787 

59 

44,328 

2,037 

1,329,827 

2,036,971 

10.85 

9.494 

7.845 

5.925 

60 

42,241 

2,098 

1,268,718 

2,098,080 

11.37 

9.951 

8.072 

6.082 

61 

40,193 

2,161 

1,205,776 

2,161,022 

11.97 

10.47 

8.371 

6.257 

62 

38,032 

2,226 

1,140,946 

2,225,852 

12.65 

11.07 

8.731 

6.464 

63 

35,806 

2,293 

1,074,170 

2,292,628 

13.43 

11.75 

9.102 

6.681 

64 

33,513 

2,361 

1,005,492 

2,361,306 

14.35 

12.56 

9,538* 6.954 

65 

31,152 

2,433 

934,550 

2,432,248 

15.44 

13.51 


7.251 

66 

28,719 

2,505 

861,583 

2,505,215 

16.75 

14.65 


7.622 

67 

26,214 

2,580 

786,427 

2,580,371 

18.35 

16.05 


8.063 

68 

23,634 

2,658 

709,016 

2,657,782 

20.35 

17.81 


8.615 

69 

20,976 

2,738 

629,283 

2,737,515 

22.93 

20.06 


*9.285 

70 

18,238 

2,819 

547,158 

2,819,640 

26.37 

23.08 



71 

15,419 

2,904 

462,569 

2,904,229 

31.19 

27.29 



72 

12,515 

2,991 

375,442 

2,991,356 

38.43 

33.63 



73 

9,524 

3,081 

285,701 

3,081,097 

50.50 

44.19 



74 

6,443 

3,174 

193.268 

3,173,530 

74.66 

65.32 



75 

3,269 

3,269 

98,062 

3,263,736 

147.1 

128.7 




Total IQO.OQQ $152,509,761 $100,000,089 
Total $252,509,850 

Which is equal to 75 annuites of $3,366,798 each. 


* The real rates of interest are 
not carried to higher rates because 
the Tables do not run higher than 
10 ^. 


31 









ANNUITIES AND AMORTIZATION TABLES 


CHAPTER VI 

LOANS REDEEMED ABOVE PAR. 

CONTENTS 

A.—When the premium is constant.—Example.—A Loan.—Nominal 
Capital.—Real or effective capital.—Capitalization rate.—Real or effective 
rate of interest.—Table of annual amortization quotas.—Tabular illustration of 
the Loan.—Synopsis of the solutions.—B.—^When the premium varies.— 
Example.—A Loan.—How to make the amortization table.—Tabular illustration 
of the redemption of bonds.—The United States Government Liberty Loan. 

-o — o — o- 

A 

WHEN The premium is CONSTANT 

The best way of demonstrating this condition is to use all through this 
chapter the following example. 

Example —Suppose Columbia University received a bequest in the form of 
an annuity of $1,000,000 for 20 years, and desires for special developments to 
borrow the actual value of this annuity by issuing bonds vf a nominal value of 
$1000, with $60 yearly interest coupons, the bonds to be redeemed in 20 years 
at $1200 each, by annual drawings on the amortization plan. 

The nominal value of the bonds must be considered as if it were $1200 
instead of $1000; and the annual income of $60 interest as an investment of 
5% instead of 6%; and the par value of $1000 printed on the bonds must not 
be taken into consideration, nor influence any of the different calculations. 

FIRST—NOMINAL CAPITAL 

To determine the nominal capital, or to find how many bonds the University 
may issue in this loan, see Table VI, page 208, which shows that the actual 
value of an annuity of $1 for 20 years @ 5%, is $12.4622099. Multiply the 
known annuity of $1,000,000, by $12.4622099=$12,462,209.90, as if the nominal 
value of each bond were $1200. 

But as the nominal value of each bond is $1000, the nominal capital will be 
$12,462,210 X1000-^1200-^$10,385,180, which divided by $1000 the nominal 
value of each bond, = 10385 bonds. 

SECOND—REAL OR EFFECTIVE CAPITAL 

To calculate the real capital, the real interest must be known. Suppose 
Columbia University is willing to borrow at 7V2%. Table VI, page 216, shows 
that the actual value of an annuity of $1. @ 71/2% for 20 years, is $10.1944844; 
therefore the actual value of an annuity of $1,000,000 will be $10,194,484.40^ 
which is the real capital. ^ 

Thus to find the actual market value, at which the bonds are issued, divide 
$10,194,484 by 10385, the number of bonds issued, which equals $980 per bond 
or 98%. 


32 



ANNUITIES AND AMORTIZATION TABLES 


Third—CAPITALIZATION rate 

Knowing the real capital of the loan, $10,194,484, the following equation 
will be used to find the capitalization rate, including interest and amortization 
quota. 

When with an annuity of $1,000,000, a real capital of $10,194,484 is 
amortized, what annuity will amortize a real capital of $100? The equation is 
as follows: 10,194,484 : 100=1,000,000 : x; therefore;c=9.809214%, the capital¬ 
ization rate. 

fourth—REAL OR EFFECTIVE RATE OF INTEREST 

Knowing the capitalization rate, 9.809214%, the rate for $1. will be 
0.09809214. In Table III, page 126, line of 20 years, it is found that this 
annuity corresponds to the real rate of interest of 7^2%, which was presupposed. 


Nominal Nominal 

Capital Capita] Re- Annuity 

Redemption Outstanding deemed $1,000,000 

Years Value Pace Value Real Capital Bonds bonds 

$1200 per bond $1000 per bond at71-2‘^. at the end of every Amortization 



JBO coupon 

$60 coupon 


every year 

year 

Interest 

quota. 

1 

12,462,210 

10,385,180 

10,194,484 

10,385 

314 

623,100 

376,800 

2 

12,085,410 

10,071,180 

9,959,074 

10,071 

330 

604,260 

396,000 

3 

11,689,410 

9,741,180 

9,706,005 

9,741 

346 

584,460 

415,200 

4 

11,274,210 

9,395,180 

9,433,956 

9,395 

363 

563,700 

435,600 

5 

10,838,610 

9,032,180 

9,141,503 

9,032 

381 

541,920 

457,200 

6 

10,381,410 

8,651,180 

8,827,116 

8,651 

401 

519,060 

481,200 

7 

9,900,210 

8,250,180 

8,489,150 

8,250 

421 

495,000 

505,200 

8 

9,395,010 

7,829,180 

8,125,837 

7,829 

442 

469,740 

530,400 

9 

8,864,610 

7,387,180 

7,735,275 

7,387 

464 

443,220 

556,800 

10 

8,307,810 

6,923,180 

7,315,421 

6,923 

487 

415,380 

584,400 

11 

7,223,410 

6,436,180 

6,864,078 

6,436 

512 

386,160 

614,400 

12 

7,109,010 

5,924,180 

6,378,884 

5,924 

537 

355,440 

644,400 

13 

6,464,610 

5,387,180 

5,857,301 

5,387 

564 

322,920 

676,800 

14 

5,787,810 

4,823,180 

5,296,599 

4,823 

592 

289,380 

710,400 

15 

5,077,410 

4,231,180 

4,693,844 

4,231 

622 

253,860 

746,400 

16 

4,331,010 

3,609,180 

4,045,883 

3,609 

653 

216,540 

783,600 

17 

3,547,410 

2,956,180 

3,349,324 

2,956 

686 

177,360 

823,200 

18 

2,724,210 

2,270,180 

2,600,524 

2,270 

720 

136,200 

864,000 

19 

1,860,210 

1,550,180 

1,795,564 

1,550 

756 

93,000 

907,200 

20 

953,010 

l794,180 

930,232 

794 

794 

47,640 

952,800 


7.538,340 12,462,000 
$20,000,340 


Fifth—Table of annual amortization quotas 

Knowing the value of the first year’s amortization quota, determined by 
deducting the interest from the annuity for the first year, the table for the 
annual amortization quotas may be made as follows: 

33 









_ ANNUITIES AND AMORTIZATION TABLES _ 

The bonds issued being 10385, the annual interest is 10385 X60=$623,100. 
Deducting this from the annuity of $1,000,000 leaves $376,900, which is the first 
year’s amortization quota. Multiply successively this amount of $376,900. by 
1.05 and divide by 1200, the redemption value of each bond, and the following 
table will result: 


Years 

Bonds 

Years 

Bonds 

1 

314 

11 

512 

2 

330 

12 

537 

3 

346 

13 

564 

4 

363 

14 

592 

5 

381 

15 

622 

6 

401 

16 

653 

7 

421 

17 

686 

8 

442 

18 

720 

9 

464 

19 

756 

10 

487 3,949 

20 

794 


— 0 — 0 — 0 — 0 — 


SYNOPSIS OP THE SOLUTIONS OF THE CALCULATIONS 
The loan of Columbia University will be as follows: 

1st The nominal capital—$10,385,180. 

2nd The bonds issued—10,385. 

3rd The real capital borrowed—$10,194,484. 

4th The capitalization rate of the loan—9.80%. 

5th The annuity payable yearly—$1,000,000. 

6th The market value of the bonds—98%. 

7th The nominal or face value of each bond—$1,000. 

8th The redemption price of each bond— $1,200. 

9th The nominal interest—6%. 

10th The real interest—7^^%. 


-O-0 — 0- 

B 

WHEN THE PREMIUM VARIES 

The difference between this kind of a loan and the preceding one is, that 
in this the premium on the bonds called for redemption, is not the same each 
year, but arbitrarily varies. 

EXAMPLE —A railroad company has an income of $200,000 per year from 
its investments, and decides to borrow the actual value of this annuity for 15 
years, by issuing bonds of a face value of $1000, yielding $40 annually, on the 
following redemption plan: 

The first 5 years the redemption value will be $1100. 

“ next 5 “ “ “ “ “ “ 1200. 

“ last 5 “ “ “ “ “ “ 1300. 


34 







ANNUITIES AND AMORTIZATION TABLES 


To find the nominal capital, or how many bonds the Company may issue; 
and to make the amortization table of this loan, the calculation must start from 
the 15th and last year with the amount (/. e. $200,000) applicable to the pay¬ 
ment of the interest and amortization quota of the bonds, which must be 
redeemed that year to extinguish the loan. 

The net disposable amount for the 15th year will be the annuity of $200,000 
covering the interest and amortization quota of the bonds still outstanding. The 
interest is $40 per bond, the redemption value is $1300; therefore to find how 
many bonds will be redeemed at the end of the 15th year, the annuity of 
$200,000 should be divided by $1340. 

$200,000-^1340=149.25 bonds 

149 bonds will be redeemed at the end of the 15th year @ $1300 each and inter¬ 
est, carrying forward 0.25 of a bond. 

NOTE—The fractional part of a bond must always be considered. 

At the 14th year, the number of bonds to be redeemed will be computed by 
multiplying 149 bonds, which will be redeemed the 15th year, by $40 interest, 
which will equal $5960, and deducting this from the annuity. 

$200,000—5960=$194,040 

which is the sum of the amortization quota and the interest on the bonds to be 
redeemed in the 14th year: therefore $194,040-j-$1340= 144.80 bonds. 

Adding 0.25 of a bond, carried forward from the 15th year, equals 145.05 bonds 
to be redeemed at the end of the 14th year. 

At the 13th year, the process will be the same as above: 

$200,000—(149+145=294X40=$11,760)=$188,240. 

$188,240-^1,340=140.50 bonds, to be redeemed at the end of the 13th year 
carrying forward 0.50 of a bond. 

At the 12th year, the process will be the same. 

$200,000—(149-M45+140=434X40=$17,360)=$182,640. 
$182,640-J-1340=136.30+.50=136.80 bonds. The fraction l)eing over one 
half will be used as a unit making 137 bonds to be redeemed at the end of the 
12th year. 

At the 11th year, it will be as follows: 

$200,000—(149-fl45-f-140-l-137=571X40=$22,840)=$177,160. 
$177,160-^-1340=132.21 bonds. 132 bonds will be redeemed at the end of the 
11th year, carrying forward 0.21 of a bond. 

At the 10th year, the divisor changes from $1340 to $1240, as it was 
understood the bonds would be redeemed at $1,200 the second period of five years. 
Therefore 

$200,000—(149-f-145-f 140+137-fl32=703X40=28120)=$171,880. 
$171,880-^-1240=138.61 bonds, plus 0.21 of a bond carried from the 11th year, 
making a total of 139 bonds to be redeemed at $1,200 each at the end of the 
10th year. 


35 



ANNUITIES AND AMORTIZATION TABLES 


By continuing these calculations to the end of the 6th year, when the 
divisor again changes to $1140, and thence up to the first year, the amortization 
table of the entire loan will appear as follows: 


Years 

Number of bonds 

Years 

Number of bor 


to be redeemed 


to be redeem 

1 

111 


973 

2 

115 

9 

134 

3 

119 

10 

139 

4 

123 

11 

132 

5 

128 

12 

137 

6 

121 

13 

140 

7 

126 

14 

145 

8 

130 

15 

149 


973 


1,949 


— u — U V — 

UNITED STATES OP AMERICA 

Capital $29,052,577,000. 


4V2% Gold Bonds. 


To be amortized in 50 years by drawings or purchases, in whole or in part, 
at the option of the United States Government. Interest payable annually 
December 15. 

Class of Bonds: Coupon bonds. 

Denomination: $100 each and numbered from 000,000,001 to 290,525,770. 

Redemption: On December first of every year a drawing will take place in 
the Treasury Department, where a number of bonds will be drawn representing 
an amount equal to the annual amortization quota of the loan. The numbers 


drawn will be called in on 

December 15 of every year, at 

the 

following redemp- 

tion values and interest: 







The first ten 

years 

the redemption will be 

@ 

102%% 

“ next ‘‘ 

« 

« 

a 

(( u 

@ 

105 % 

(( (< <( 



it 

<( ii 

@ 

107%% 

<( (( (( 

<; 

n 

(< 

it it 

@ 

110 % 

“ last ‘‘ 

(( 


(( 

a a 

@ 

112%% 


Security: For the service of the loan (payment of the interest and amorti¬ 
zation quota) the United States Government has allocated during the life of the 
loan the revenues from war taxation estimated to amount annually to one and one- 
half billion dollars. Should the proceeds of these revenues show a deficit from the 
the amount required for the service of the loan, the Secretary of the Treasury 
may be empowered to appropriate any surplus existing in the Treasury Depart¬ 
ment, or the United States Government may agree to provide additional income 
by further taxation. But should the proceeds of these revenues show a surplus 
above the amount required for the service of the loan, an additional number of 
bonds will be drawn, payable at the specific redemption value of that year when 

36 




ANNUITIES AND AMORTIZATION TABLES 


the surplus occurs; and further, if the market value is below the redemption 
value mentioned for that year, the United States Government has the privilege 
of buying in the open market a number of bonds representing an amount equal 
to the surplus. The bonds called in and redeemed by this surplus will be cred¬ 
ited to the last year’s amortization quota. 

The loan is as follows:— 

Suppose that the United States Government raises by taxation an amount 
estimated to be one and one half biUion dollars annually for fifty years, and de¬ 
sires to issue a Consolidated War Loan, by issuing bonds of a nominal value of 
$100 each, yielding $4.50 annual interest, the bonds to be redeemed with 
premiums, on the plan mentioned above, by yearly drawings. 

Bonds issued. 290,525,770 

Nominal and real capital. $29,052,577,000 

Nominal rate of interest. 41^% 

Market value of bonds. $100 

The chart of the loan will be as follows:— 



Outstanding bonds 


Number of bonds 

Outstanding bonds 

Years 

at the beginning of 


redeemed 

at end of 


every year. 

Till6i0st« 

every year 

every year 

50 

12,820,513 

57,692,308.50 

12,820,513 


49 

25,147,929 

113,165,680.50 

12,327,416 

12,820,513 

48 

37,001,214 

166,505,463.00 

11,853,285 

25,147,929 

47 

48,398,475 

217,793,137.50 

11,397,261 

37,001,214 

46 

59,357,508 

267,108,786.00 

10,959,033 

48,398,475 

45 

69,894,441 

314,524,984.50 

10,536,933 

59,357,508 

• 44 

80,026,706 

360,120,177.00 

10,132,265 

69,894,441 

43 

89,769,269 

403,961,710.50 

9,742,563 

80,026,706 

42 

99,137,118 

446,117,031.00 

9,367,849 

89,769,269 

41 

108,144,665 

486,650,992.50 

9,007,547 

99,137,118 

40 

116,968,674 

526,359,033.00 

8,824,009 

108,144,665 

39 

125,472,089 

564,624,400.50 

8,503,415 

116,968,674 

38 

133,641,308 

601,385,886.00 

8,169,219 

125,472,089 

37 

141,489,466 

636,702,597.00 

7,848,158 

133,641,308 

36 

149,029,181 

670,631,314.50 

7,539,715 

141,489,466 

35 

156,272,576 

703,226,592.00 

7,243,395 

149,029,181 

34 

163,231,296 

734,540,832.00 

6,958,720 

156,272,576 

33 

169,916,529 

764,624,380.50 

6,685,233 

163,231,296 

32 

176,339,024 

793,525,608.00 

6,422,495 

169,916,529 

31 

182,509,106 

821,290,977.00 

6,170,082 

176,339,024 

30 

188,569,008 

848,560,536.00 

6,059,902 

182,509,106 

29 

194,385,432 

874,734,444.00 

5,816,424 

188,569,008 

28 

199,968,160 

899,856,720.00 

5,582,728 

194,385,432 

27 

205,326,582 

923,969,619.00 

5,358,422 

199,968,160 

26 

210,469,710 

947,113,695.00 

5,143,125 

205,326,582 


37 












ANNUITIES AND AMORTIZATION TABLES 


YeJirs 

Outstanding bonds 
at the beginning of 

Annual 

Number of bonds 
redeemed 

Outstanding bonds 
at end of 


every year. 

xlJl'CX vSl* 

every year 

every year 

25 

' 215,406,195 

969,327,877.50 

4,936,485 

210,469,710 

24 

220,144,339 

990,649,525.50 

4,738,144 

215,406,195 

23 

224,692,111 

1,011,114,499.50 

4,547,772 

220,144,339 

22 

229,057,260 

1,030,757,670.00 

4,365,049 

224,692,111 

21 

233,246,924 

1,049,611,158.00 

4,189,664 

229,057,260 

20 

237,360,064 

1,068,120,228.00 

4,113,140 

233,246,924 

19 

241,304,171 

1,085,868,769.50 

3,944,107 

237,360,064 

18 

245,086,191 

1,102,887,859.50 

3,782,020 

241,304,171 

17 

248,712,786 

1,119,107,537.00 

3,626,595 

245,086,191 

16 

252,191,256 

1,134,860,652.00 

3,478,470 

248,712,786 

15 

255,525,862 

1,149,866,379,00 

3,334,606 

252,191,256 

14 

258,723,429 

1,164,255,430.50 

3,197,567 

255,525,862 

13 

261,789,589 

1,178,053,150.50 

3,066,160 

258,723,429 

12 

264,729,743 

1,191,283,843.50 

2,940,154 

261,789,589 

11 

267,549,434 

1,203,972,453.00 

2,819,691 

264,729,743 

10 

270,316,047 

1,216,422,211.50 

2,766,613 

267,549,434 

9 

272,966,307 

1,228,348,381.50 

2,650,260 

270,316,047 

8 

275,505.107 

1,239,772,981.50 

2,538,800 

272,966,307 

7 

277,937,135 

1,250,717,257.50 

2,432,028 

275,505,107 

6 

280,266,880 

1,261,200.962.00 

2,329,745 

277,937,135 

5 

282,498,647 

1,271,243,911.50 

2,231,767 

280,266,880 

4 

284,636,554 

1,280,864,493.00 

2,137,907 

282,498,647 

3 

286,684,549 

1,290,080,470.50 

2,047,995 

284,636,554 

2 

288,646,414 

1,298,908,863.00 

1,961,865 

286,684,549. 

1 

290,525,770 

1,307,365,965.00 

1,879,356 

288,646,414 


290,525,770 bonds 


38 










ANNUITIES AND AMORTIZATION TABLES 


CHAPTER VII. 

LOANS REDEEMED AT PAR WITH PREMIUMS OR PRIZES. 

CONTENTS 

Features of bonds carrying lottery privileges.—When the premium is 
divided equally among the bonds to be redeemed.—Example.—New York 
City’s loan.—Conditions of the loan.—Annuity of the premiums.—Capitalization 
rate.—Real rate of interest.—When the premium is given to only a certain 
number of the bonds redeemed.—Example.—Nominal capital.—When the 
premium is given to a fixed number of bonds and not divided equally among 
them, but given in the form of prizes.—Example.—Table of prizes.—Solu¬ 
tion.—Amortization Table of the loan.—Tabular illustration of the bonds draw¬ 
ing prizes.—Variations of the loans. 

This chapter will be a consideration of the class of bonds carrying lottery 
privileges, viz;—Ville de Paris; Credit Foncier de France; Credit Fonder Egyp- 
tien; Comptoir Agricole Hongrois; Rural Loans of the National Bank of Greece; 
etc. These bonds are, and always have been created under the sanction and 
patronage of their respective governments, and offer to the holders an absolutely 
safe investment with the additional attraction of the lottery privilege, which 
provides a certain satisfaction for the ever existent human proclivity for specu¬ 
lation, but in the unique manner by which the holder of the bonds cannot possibly 
lose his money, and even enjoys a good income on the price paid so long as it is 
held. The author ventures the belief that if the real character and operative 
value of this class of bonds were more clearly understood and more broadly ap¬ 
preciated in America, it would gradually and effectually remove the unfortunate 
prejudice and actual illegality of the recognition of any method of investment 
associated with a prize or lottery privilege. 

These features have been long existent in Europe, where they are universally 
popular and attended by such success for both the issuing companies and the in¬ 
vestors, all elements of the investment and the capital being fully considered, as 
will be seen herein, that a thorough investigation of the matter by Federal 
authorities would be a timely and wise procedure, particularly in view of the very 
radical and serious problems that the future has in store for every financier and 
investor. 

The most sensational issue of these bonds, was that of January, 1912, by 
the Credit Foncier de France, “ Obligations communales,” of fcs. 500,000,000, 
divided into 2,000,000 bonds of fcs. 250 each, running 70 years and bearing 3% 
interest. This issue was found to be nineteen times over-subscribed, when the 
public subscriptions were counted. 


39 




ANNUITIES AND AMORTIZATION TABLES 


FEATURE. 

An amount is distributed among the bonds drawn to be redeemed. This 
amount, which is to be distributed in prizes or premiums, may be equal for each 
bond or may be unequal. 


— o — o — o- 

FIRST PROBLEM. 

When the yearly premium is divided equally among the bonds to be redeemed. 

EXAMPLE:—The City of New York wishes to make a loan of $75,000,000 
by an issue of bonds that will give a premium of 5% at the underwriting of the 
issue, to run for 60 years, the par value of the bonds to be $100, bearing inter¬ 
est @3% per annum, and in addition an aggregate of $200,000 to be divided 
in equal prizes annually among the bonds drawn by lot. The nominal capital of 
the loan is $75,000,000. The real amount of the borrowed capital less 5% pre¬ 
mium is $71,250,000. The number of bonds sold at $95. each and outstanding 
is 750,000. 

CONDITIONS OF THE LOAN AND SOLUTION BY THE TABLES. 

ANNUITY. 

The annuity or annual instalment of the loan will be as follows: 

Table III, page 112, shows that the annuity of $1. for 60 years at 3% is 
0.036133 ; therefore the annuity of $75,000,000 will be 

0.036133 X75,000,000=$2,709,975. 

To this amount add the yearly premiums of $200,000, making a total annuity of 
$2,909,975, which is divided for the first year as follows: 

(a) for the interest of $75,000,000 at 3% $2,250,000 

(b) Amortization quota (4600 bonds at $100) 459,975 

(c) Prizes awarded annually . . . 200,000 

Total annuity $2,909,975 

This, of course, will vary in detail each succeeding year, but will be the same in 
the aggregate each year. 

ANNUITY OF THE PREMIUMS. 

To find the annuity of the premiums corresponding to a capital of $100, 
the problem is as follows: The annuity of a capital of $75,000,000, interest, 
amortization quota, and premiums included, is $2,909,975 ; therefore the annuity 
of $100 will be: 


2,909,975 X 100-^-75,000,000=3.879966. 

Table III, page 112, shows that the annuity of $1. for 60 years at 3% is 
0.036133 ; therefore of $100 it is 3.6133. Thus the difference between the an¬ 
nuities of 3.879966 and 3.6133, which is 0.266666, represents the portion of the 
total annuity, devoted to the premiums for every nominal, borrowed, capital 
of $100. 


40 




ANNUITIES AND AMORTIZATION TABLES 


CAPITALIZATION RATE. 

When for a nominal capital of $100 there is an annuity of 3.879966, for an 
effective capital of $95 it will be 3.879966X100-^95=4.084175 per cent, which 
is the capitalization rate, including interest, amortization quota and premiums 

— o — o — o- 

REAL RATE OP INTEREST. 

To find the real rate of interest, refer to the line of 60 years, Table III, 
page 112, where it is found that the capitalization rate of 4.084175 per $100 
capital, including interest, amortization quota and premiums, is between 4.008866 
and 4.212670 per $100 capital, representing a real rate of interest of 3%% and 
3%% respectively. Therefore the real rate of interest is between 3^2% and 
3%%. The exact rate may be found as follows: The difference between 
4.008866 and 4.212670 is 0.203804, representing 0.25%. The difference 
between 4.084175 and 4.212670 being 0.128495, will represent 

0.128495X0.25-^-0.203804=0.157615%. 

Add this to 3.50%, which makes 3.657615% the real rate of interest of the loan. 

Consequently the City of New York borrowed $75,000,000 at the real rate 
of interest of 3.657615%. 


— o — o — o- 

SECOND PROBLEM. 

When the yearly premium is given in the form of prizes to only a certain 
number of bonds to be redeemed by drawings. 

The prizes ordinarily cover the redemption value of the bonds and the in¬ 
terest coupon. Consequently the prizes are not worth their intrinsic value, but 
a value diminished by the face value of the bond and the interest coupon, since 
the bondholder winning a prize accepts the prize in lieu of his bond. 

EXAMPLE: —The same example as above is used, with the difference that 
the premium of $200,000 is not given to all the bonds to be redeemed every year, 
but only to 100 of these bonds to be drawn annually by lot. 

— o o — o 

PRIZE ACCOUNT. 

In this case the bonds to be redeemed by prizes are ordinarily the first 100 
bonds drawn by lot, and are primed i.e. paid off by the prizes only; therefore 
the intrinsic value of $200,000 of premium is diminished, 1st., by the face value 
of $100 per bond, and 2nd., by the 3% interest coupon of each bond, viz: 
$200,000 less 100 bonds of $100 par value each, or $10,000=$190,000. 
$190,000 less $3 interest coupon for each of the 100 bonds, or $300=$189,700; 
and the difference of $10,300 is employed for the service of the interest and 
amortization quota of the loan. 


4 


41 




ANNUITIES AND AMORTIZATION TABLES 


ANNUITY. 

For this reason instead of an annuity of $2,709,975 for the interest and 
amortization quota of the loan, there will be $2,709,975+$10,300=$2,720,275. 

NOMINAL CAPITAL OR AMOUNT OF BONDS TO BE ISSUED. 

Knowing the annuity of the loan to be $2,720,275 for 60 years at 3%, 
Table III, page 112, line 60 years shows that @ 3% a capital of $1. will have 
an annuity of 0.036133; therefore an annuity of $2,720,275. will be. 

2,720,275^0.036133=75,285,058, 
which amount divided by 100, gives 752,851 bonds to be issued. 


— o — o 




THIRD PROBLEM. ' 

When the yearly premium is given to a fixed number of bonds and not 
divided equally among them, but given in the form of unequal prizes; and when 
the drawings are held more than once a year. 

The prizes of the primed bonds contain always the face value and the in¬ 
terest coupon of the bonds. 

EXAMPLE:—The same example under a different form is as follows: 

The City of New York has an annuity of $2,909,975 for 60 years, and desires 
to borrow on this annuity, for this period, funds to build a new subway, the 
bonds to have a par or redemption value of $100 each, to bear 3% interest per 
annum, besides distributing prizes to a fixed number of the bonds, in several 
drawings each year, for the purpose of attracting small investors, and without 
imparing the security of the capital. What is the nominal capital of the loan; 
or how many bonds may the City of New York issue? 

To solve this example, the table of the prizes must first be made. The 
amount to be given in prizes to each bond is usually fixed arbitrarily. Only a 
very small portion of the annuity should be used for this purpose, because if the 
amount given in prizes is too large the remaining amount of the annuity will 
not be sufficient for the interest and amortization quota of the loan. In such an 
event, it will be necessary to raise the conditions of the issue, either in the 
price of the bonds, or the time of the loan, or both. 

Suppose a table of prizes as follows: 

42 





ANNUITIES AND AMORTIZATION TABLES 


FOR THE FIRST THREE YEARS, FOUR DRAWINGS PER ANNUM. 


1st Drawing, January 1st. 

2nd Drawing, April 1st. 

Niunber of bonds 
to be drawn 

Prizes 

Total amount 
of Prizes 

Number ctf bonds 
to be drawn 

Prizes 

Total amount 
of Prizes 

1 

$100,000 

$100,000 

1 

$50,000 

$50,000 

1 

10,000 

10,000 

1 

10,000 

10,000 

2 

5,000 

10,000 

1 

5,000 

5,000 

2 

2,500 

5,000 

3 

2,500 

7,500 

4 

1,000 

4.000 

4 

1,000 

4,000 

10 

500 

5.000 

10 

500 

5,000 

20 


$134,000 

20 


$81,500 

3rd Drawing, July 1st. 

4th Drawing, October 1st. 

Number of bonds 
to be drawn 

Prizes 

Total amount 
of Prizes 

Number of bonds 
to be drawn 

Prizes 

Total amount 
of Prizes 

1 

$75,000 

$75,000 

1 

$50,000 

$50,000 

1 

7,500 

7,500 

1 

7,500 

7,500 

2 

5,000 

10.000 

1 

4,000 

4,000 

2 

2,500 

5,000 

3 

2,500 

7,500 

4 

1,000 

4,000 

4 

1,000 

4,000 

10 

500 

5,000 

10 

500 

5,000 

20 


$106,500 

20 


$78,000 


Grand 

Total for the first Three Years. 


Three 

first drawings of 20 Prizes 

, 60 Prizes @ 

$134,000 

$402,000 


second ” 

” 20 

60 ” 

81,500 

244,500 

5? 

third 

” 20 

60 ” 

106,500 

319,500 

>> 

Fourth 

” 20 

60 ” 

78,000 

234,000 




240 

$1,200,000 

FOR THE 

FOLLOWING 

SEVEN YEARS, TWO DRAWINGS PER ANNUM 

1st Drawing, January 

10th. 

2nd Drawing, July 10th. 

Number cf bonds 
to be drawn 

Prizes 

Total amount 
of Prizes 

Number of bonds 
to be drawn 

Prizes 

Total amount 
of Prizes 

1 

$40,000 

$40,000 

1 

$25,000 

$25,000 

1 

5,000 

5,000 

1 

5,000 

5,000 

2 

2,500 

5,000 

6 

1,000 

6,000 

16 

500 

8.000 

12 

500 

6,000 

20 


58,000 

20 


$42,000 


43 




























ANNUITIES AND AMORTIZATION TABLES 
Grand Total for the Seven Years 


Seven first drawings of 20 Prizes, 140 Prizes @ $58,000 $406,000 
” second ” ” 20 ” ” ” 42,000 294,000 

280 $700,000 


FOK THE FOLLOWING FIFTEEN YEARS, THREE DRAWINGS 
PER ANNUM. 


1st Drawing, January 1st. 2nd Drawing, May 1st. 

Number of bonds ^ . Total amount Number of bonds _ . Total amount 

to be drawn rnzes Prizes to be drawn Prizes ^ Prizes 


1 

$25,000 

$25,000 

1 

$20,000 

$20,000 

1 

6,000 

6,000 

1 

4,000 

4,000 

2 

2,500 

5,000 

1 

2,000 

2,000 

6 

1,000 

6,000 

3 

1,000 

3,000 

30 

500 

15,000 

34 

500 

17,000 

w 


$57,000 

40 


$46,000 


3rd Drawing, September 1st. 

Number of bonds q • Total amount 

to be drawn Prizes Prizes 


1 

1 

2 

6 

M. 

40 


$25,000 $25,000 

6,000 6,000 

2,500 5,000 

1,000 6,000 

500 15,000 

$57,000 


Grand Total for the Fifteen Years. 


Fifteen first drawings of 40 Prizes, 600 Prizes @ $57,000 $855,000 
” second ” ” 40 ” 600 ” 46,000 690,000 

third ” ” 40 ”_^ ” 57,000 855,000 

1,800 $2,400,000 


44 




















ANNUITIES AND AMORTIZATION TABLES 


FOR THE FOLLOWING TWENTY-FOUR YEARS, FOUR DRAWINGS 

PER ANNUM. 


1st Drawing, January 1st. 


2nd drawing, April 1st. 

Number of bonds 
to be drawn 

Prizes 

Total amount 
of Prizes 


Number of bonds 
to be drawn 

Prizes 

Total amount 
of Prizes 

1 

$60,000 

$60,000 


1 

$25,000 

$25,000 

1 

5,000 

5,000 


1 

5,000 

5,000' 

4 

2,500 

10,000 


1 

2,500 

2,500 

6 

1,000 

6,000 


8 

1,000 

8,000 

18 

500 

9,000 


.9 

500 

9,500 

30 


$90,000 


30 


$50,000 

3rd Drawing, July 1st. 


4th Drawing, October 1st. 

Number bonds 
to be drawn 

Prizes 

Total amount 
of Prizes 


Number of bonds 
to be drawn 

Prizes 

Total amount 
of Prizes 

1 

$50,000 

$50,000 


1 

$25,000 

$25,000 

1 

5,000 

5,000 


1 

5,000 

5,000 

2 

2,500 

5,000 


1 

2,500 

2,500 

7 

1,000 

7,000 


8 

1,000 

8,000 

19 

500 

9,500 


19 

500 

9,500 

30 


$76,500 


30 


$50,000 


Grand Total for the Twenty-four 

Years. 


24 first drawings of 

30 Prizes, 720 

Prizes @ 

$90,000 $2,160,000 

24 second 


30 ” 

720 

if If 

60,000 1,200,000 

24 third 

»> » 

30 ” 

720 

ff ff 

76,500 1,836,000 

24 fourth 


30 ” 

720 

ff » 

60,000 1,200,000 


2,880 $6,396,000 


FOR THE LAST ELEVEN YEARS, TWO DRAWINGS PER ANNUM. 


1st Drawing, January 15th. 2nd Drawing, July 15th. 


Number of bonds 
to be dravm 

Prizes 

Total amount 
df Prizes 

Number of bonds 
to be drawn 

Prizes 

Total amount 
of Prizes 

1 

$40,000 

$40,000 

1 

$20,000 

$20,000 

2 

10,000 

20,000 

1 

10,000 

10,000 

3 

5,000 

15,000 

1 

5,000 

5,000 

11 

1,000 

11,000 

14 

1,000 

14,000 

15 

500 

7,500 

15 

500 

7,500 

32 


$93,500 

32 


$56,500 


Grand Total for 

the Eleven Years. 



Eleven first drawings of 32 Prizes, 352 Prizes @ 

$93,500 

$1,028,500 

ff 

second ” 

” 32 ” 

352 ” 

56,500 

621,500 




704 


$1,650,000 


45 






























ANNUITIES AND AMORTIZATION TABLES 


In the above table of prizes, it is evident, 1st, there are more than one 
drawing each year; and 2nd, the prizes are not of equal amounts. But for the 
purpose of following the same kind of problem, and also for maintaining the 
general conditions of the loan, and to make it very attractive to the investor, 
the average amount of prizes was purposely arranged so as not to vary greatly 
from $200,000 annually. 

SOLUTION. 

The conditions of the loan are as follows: (/) Annuity, $2,909,975. 
(2) Time, 60 years. (3) Rate of interest, 3%. {4) Prizes shown by the 

table. (5) What is the nominal value of the loan; or how many bonds of a 
$100 par value may the City of New York issue? The Amortization table of 
this loan will show 1st, the capital; 2nd, the interest; 3rd, the amortization 
quota; 4th, the value of the prizes; and 5th, the bonds primed, or paid off by 
prizes for every year from 1 to 60. The interest is paid annually. The bonds 
paid off by prizes by the semi-annual, or quarterly drawings, bear no interest, 
the interest coupons being detached and payable only on the last day of the 
year., 

The Amortization Table will start at the 60th and last year, by accounting 
the net disposable amount, after deducting the amount of prizes successively for 
each year, as follows: 

The net disposable amount for the 60th year for the interest and amortiza¬ 
tion quota will be the annuity of $2,909,975, less the prizes $150,000=$2,759,975. 
Therefore, the number of bonds to be paid off at the end of the 60th year at par 
and interest or 103, will be 2,759,975-^103=26,795.87. The decimal being 
more than one-half, it will be taken as a whole bond, and therefore 26,796 bonds 
will be redeemed at par and interest. To this number of 26,796 bonds add the 
64 bonds, which were drawn and received the $150,000 prizes in place of their 
par and interest, making a total of 26,860 bonds paid off the 60th year. 

For the 59th year, first account for the 3% interest on the 26,860 bonds, 
which will be paid off the 60th year, amounting to $80,580, which must be de¬ 
ducted from the annuity of $2,909,975. From the remaining amount of 
$2,829,395 deduct the prizes of $150,000, leaving $2,679,395, which represents 
the amortization quota and interest on 26,013 bonds for the 59th year. 

(a) 60th year 2,909,975—150,000=2,759,975^103=26,795.87 bonds. 

To these 26,796 bonds add the 64 bonds drawing $150,000 prizes = 26,860. 

{h) 59th year 2,909,975—(26,860 X3=80,580)=2,829,395—150,000= 
2,679,395-^-103=26,013.54. bonds. 

To these 26,013 bonds add the 64 bonds drawing $150,000 prizes=26,077. 

(c) 58th year 2,909,975—(26,860+26,077=52,937X3=158,811)= 
2,751,164—150,000=2,601,164-^-103=25,254 bonds. 

To these 25,254 bonds add the 64 bonds drawing the $150,000 prizes=25,318. 

In continuing these calculations up to the first year, the Table of Amorti¬ 
zation of the loan is as follows: 


46 




1 

2 

3 

4 

6 

6 

7 

8 

9 

10 

H 

12 

13 

14 

15 

16 

17 

18 

19 

20 

21 

22 

23 

24 

25 

26 

27 

28 

29 

.30 

31 

.32 

33 

34 

35 

36 

37 

38 

39 

40 

41 

42 

43 

44 

45 

46 

47 

48 

49 

50 

51 

52 

53 

54 

55 

56 

57 

58 

59 


ANNUITIES AND AMORTIZATION TABLES 


AMORTIZATION TABLE 


Interest on 
outstanding 
bonds at the 
end of each 
year 

Amortization quota Amount 
prizes of 

not prizes 

included 

Annuity 

Number of 
outstanding 
bonds at the 
end of each 
Year 

Total 

Number of Number of number of 
amortized primed amortized 

bonds bonds and primed 

bonds 

2,248,200 

261,775 

400,000 

2,909,975 

749,400 

2,542 

80 

2,622 

2,240,100 

269,875 

400,000 

746,700 

2,620 

80 

2,700 

2,231,757 

278,218 

400,000 


743,919 

2,620 

80 

2,781 

2,214,285 

595,690 

100,000 


738,095 

5,784 

40 

5,824 

2,196,288 

613,687 

100,000 


732,096 

6,969 

40 

5,999 

2,177,754 

632,221 

100,000 

909,975 

725,918 

6,138 

40 

6,178 

2,158,662 

651,313 

100,000 

719,554 

6,324 

40 

6,364 

2,139,000 

670,975 

100,000 


713,000 

6,514 

40 

6,554 

2,118,747 

691,228 

100,000 


706,249 

6,711 

40 

6,751 

2,097,885 

712,090 

100,000 


699,295 

6,914 

40 

6,954 

2,077,950 

672,025 

160,000 

2,909,975 

692,650 

6,525 

120 

6,645 

2,057,415 

692,560 

160,000 


685,805 

6,726 

120 

6,845 

2,036,268 

713,707 

160,000 


678,856 

6,929 

120 

7,049 

2,014,485 

735,490 

160,000 


671,495 

7,141 

120 

7,261 

1,992,048 

767,927 

160,000 


664,016 

7,359 

120 

7,479 

1,968,939 

781,036 

160,000 

2,909,975 

656,313 

7,583 

120 

7,703 

1,945,134 

804,841 

160,000 


648,378 

7,185 

120 

7,935 

1,920,618 

829,357 

160,000 


640,206 

8,052 

120 

8,172 

1,895,367 

854,608 

160,000 


631,789 

8,297 

120 

8,417 

1,869,357 

880,618 

160,000 


623,119 

8,550 

120 

8,670 

1,842,567 

907,408 

160,000 

2,909,975 

614,189 

8,810 

120 

8,930 

1,814,973 

935,002 

160,000 


604,991 

9,078 

120 

9,198 

1,786,551 

963,424 

160,000 


695,517 

9,354 

120 

9,474 

1,757,277 

992,698 

160,000 


685,795 

9,638 

120 

9,758 

1,724,124 

1,022,851 

160,000 


575,708 

9,931 

120 

10,051 

1,699,263 

944,212 

266,500 

2,909,975 

666,421 

9,167 

120 

9,287 

1,670,565 

972,910 

266,500 


656,855 

9,446 

120 

9,566 

1,641,006 

1,002,469 

266,500 


647,002 

9,733 

120 

9,853 

1,610,559 

1,032,916 

266,500 


536,853 

10,029 

120 

10,149 

1,579,200 

1,064,275 

266,500 


526,400 

10,333 

120 

10,453 

1,546,902 

1,096,573 

266,500 

2,909,975 

515,634 

10,646 

120 

10,766 

1,513,632 

1,129,843 

266,500 


504,544 

10,970 

120 

11,090 

1,479^366 

1,164,109 

266,500 


493,122 

11,302 

120 

11,422 

1,444,071 

1,199,404 

266,500 


481,357 

11,645 

120 

11,765 

l'407,tl7 

1,235,758 

266,500 


469,239 

11,998 

120 

12,118 


1,370,271 
1,331,703 
1,291,980 
1,251,063 
1,208,919 
1,165,509 
1,120,800 
1,074,747 
1,027,314 
978,459 
928,137 . 
876,306 
822,921 
767,931 
707,973 

646,215 

582,606 

517,086 

449,601 

380,100 

308,505 

234,765 

158,811 

80,580 


1,273,204 

1,311,772 

1,351,495 

1,392,412 

1,434,556 

1,477,966 

1,522,675 

1,568,728 

1,616,161 

1,665,016 

1,715,338 

1,767,169 

1,820,554 

1,875,544 

2,052,002 

2,113,760 

2,177,369 

2,242,889 

2,310,374 

2,379,875 

2,451,470 

2,525,210 

2,601,164 

2,679,395 

2,759,975 


266,500 

266,500 

266,500 

266,500 

266,500 

266,500 

266,500 

266,500 

266,500 

266,500 

266,500 

266,500 

266,500 

266,500 

150,000 

150,000 

150,000 

150,000 

150,000 

160,000 

150,000 

150,000 

150,000 

150,000 

150,000 


2,909,975 


2,909,975 


2,909,975 


2,909,975 


2,909,975 


456,757 

443,901 

430,660 

417,021 

402,973 

388,503 

373,600 

358,249 

342,438 

326,153 

809,379 

292,102 

274,307 

255,977 

235,991 

215,405 

194,202 

172,362 

149,867 

126,700 

102,835 
78,255 
. 52,937 
26,860 


12,362 

12,736 

13,121 

13,519 

13,928 

14,350 

14,783 

15,231 

15,691 

16,165 

16,654 

17,157 

17,675 

18,210 

19,922 

20,522 

21,139 

21,756 

22,431 

23,103 

23,801 

24,516 

25,254 

26,013 

26,796 


120 

120 

120 

120 

120 

120 

120 

120 

120 

120 

120 

120 

120 

120 

64 

64 

64 

64 

64 

64 

64 

64 

64 

64 

64 


12,482 

12,856 

13,241 

13,639 

14,048 

14,470 

14,903 

15,351 

15,811 

16,285 

16,774 

17,277 

17,795 

18,330 

19,986 

20,586 

21,203 

21,840 

22,495 

23,167 

23,865 

24,580 

25,318 

26,077 

26,860 


>,403,334 + 76.849,166 + 12,346,000 = 174,598,500 


746,118 + 5,904 = 752,022 


47 














ANNUITIES AND AMORTIZATION TABLES 


This amortization table of New York City’s loan shows: 1st, the interest 
due and payable at the end of each year. 2nd, the amortization quota of each 
year which will extinguish the loan at the end of 60 years. 3rd, the amount of 
prizes given every year. 4th, the annuity which covers the interest, amortization 
quota and prizes for every year successively. 5th, the amount of outstanding 
oonds at the end of each year. 6th, the amount of paid off bonds each year. 
7th, the amount of primed bonds, paid off by prizes every year. 8th, the total 
amount of amortized and primed bonds, which equal the yearly amortization quota. 

Consequently the City of New York must issue for this loan 752,022 bonds 
of $100 face value each. The nominal capital of the loan will be $75,202,200, 
from which 746,118 bonds will be called in by successive drawings, and paid off 
at par and interest; and 5,904 bonds will draw 5,904 prizes of a total value of 
$12,346,000 as follows: 


3 Prizes 

of $100,000 each 

6 Prizes 

of $7,500 each 

3 

M 


75,000 „ 

30 

55 

„ 6,000 „ 

24 

?> 

55 

60,000 „ 

169 

55 

„ 5,000 „ 

30 

)) 

55 

50,000 „ 

18 

55 

„ 4,000 „ 

18 

)) 

55 

40,000 „ 

296 

55 

„ 2,500 „ 

85 

J? 

55 

25,000 „ 

15 

55 

„ 2,000 „ 

26 

5) 

55 

20,000 „ 

1286 

55 

„ 1,000 „ 

39 


55 

10,000 „ 

3856 

55 

„ 500 „ 


There are also the following variations that may be used for loans of this 
class, viz: the prizes may be drawn yearly, semi-annually, every four months, 
quarterly or monthly; and the interest may be payable annually, semi-annually 
or quarterly, whichever method will make the loan more attractive to the public. 




ANNUITIES AND AMORTIZATION TABLES 


CHAPTER VIII. 


THE DETERMINATION OF THE INCOME RATE OF AN INVESTMENT 
WHEN THE BOND OR OBLIGATION IS BOUGHT AT A FIXED PRICE. 

CONTENTS 


When the redemption date is known.—Example.—Method of substituting 
the premium by increasing the annual income.—Problem. What is the increase 
of the income which will amortize the premium.—Example.—Problem. Deter¬ 
mination of the purchase price of a bond at a fixed income rate.—Example.— 
Direct solution by the tables.—Calculation of parities.—Example.—Direct solu¬ 
tion by the tables.—When the redemption date is not known.—Irredeemable 
bonds.—Amortized bonds.—Real or effective rate of interest.—Mathematical 
date.—Example.—Probable date.—Example. 


.<4.—WHEN THE REDEMPTION DATE IS KNOWN. 


To find the income rate, or how much an investment nets, is to determine 
the real or effective rate, which includes the premium, /.e., the difference between 
the purchase price and the redemption value of the bond. 

This calculation is important because it offers the investor a basis for a com¬ 
parison of the earning power of two or more bonds, without, however, considering 
any other feature. 

EXAMPLE:—A 3%, 30 year, $1,000 bond is offered at $600; what is the in¬ 
come rate; or how much does it net ? This bond, at first sight, would seem to 
net 5%; but the real rate will be found to be above 5%, because, as will appear, 
$600 is the market value of the bond and not its face or redemption value * 

The only way of solving this example is by trial and approximation. 

It is known in the beginning that the income rate is above 5%; consequently 
a trial will be made @ 5y2% or 5.50%. 

The algebraic equation mentioned in the NOTE, expressed in the figures of 
this example will read: 

1 (1000—600) (1.055—1) , 

I.UOD 600(1.055—D—1000(1.03—l)"^^ 

The equation condensed reads: 


1.055^=; 


400X0.055 


600 X 0.055—1000 X 0.03 


99 

=—+1=8.33333 


♦MARGINAL NOTE—The following algebraic equation is applicable to this case. 


Q»= 


(c—g) (q —1) I ^ 

a(q —1)—c(p—1)”^ ’ 


in which are the following elements: 
c=the par or redemption value. 
a=the market price. 

p=the unit plus its nominal rate of interest. 
nT=the time. 

q=the unit plus the income rate, in this case the unknown quantity. 
c(p—l)==the nominal annual income. 


49 







ANNUITIES AND AMORTIZATION TABLES 


Table I, page 93, shows that 1.055^, or $1. invested @ 5 V 2 % compound 
interest for, 30 years, becomes 4.983935; therefore the equation reads, 
4.983965=8.3333. This is impossible, because the second member of the equa¬ 
tion is superior to the first one. 

if 5%% or 5.75% be tried the equation will read: 

1 057530=__+1=M+i=6 1111 

i.U0<0 600X0.0575—1000X0.03^^ 4.5^^ yj.Li-i-x 


Table I, page 43, shows that 1.0575^, or $1. invested @ 5%% com¬ 
pound interest for 30 years, becomes 5.350717; therefore the equation reads, 
5.350717=6.1111. Again the second member of the equation is superior to the 
first; consequently the rate of 5T^s% or 5.875% must be tried. The equation 
will now read: 


i.uoo^o —600X0.05875—1000X0.03^ 5.25^^ 

Table I, page 43, shows that 1.05875^°, or $1. invested @ 5%% com¬ 
pound interest for 30 years, becomes 5.543729; therefore the equation reads, 
5.543729=5.47619. In this case the the first member of the equation is superior 
to the second; consequently, the income rate of the investment is between 5%% 
and 5%%, and nearer the latter. This result must be considered satisfactory to 
the investor and banker as well. 


The same calculations and trials on a larger scale may be made with logar¬ 
ithms, and the result after trying several rates will be found in this case to be 
5.86% to 5.865%. The value of 1.05865^, or $1. invested at 5.865% compound 
interest, is by logarithms 5.52805, which is the first member of the equation; 
and by using this figure in the second part of the equation, the second member 
is found to be 5.52023; therefore, 5.52805=5.52023. This being the nearest 
approximation that can be obtained, the income rate of this investment is be¬ 
tween 5.86% and 5.865%. 


—o—o—o— 


METHOD OF SUBSTITUTING THE PREMIUM BY INCREASING 
THE ANNUAL INCOME. 

PROBLEM. 

What is the annuity, or what is the annual increase of the income, which will 
amortize the premium, or the difference between the purchasing price and the 
redemption value of a bond, knowing the time and the interest rate of the bond; 
or what amount must be invested every year for the known period and rate of 
interest, for the sinking fund, which will increase to the full amount of the 
premium?* 


♦MARGINAL NOTE—The following algebraic equation is applicable to this case. 

I) from which A — 

^ q—1 ^ q^—1 

The elements are as follows: 

c=the premium or the difference between the market price and the redemption value. 
a=the annuity or the yearly sinking fund. 
q=the unit plus the interest rate of the bond. 
n=the time. 


50 








ANNUITIES AND AMORTIZATION TABLES 


EXAMPLE:—Using the foregoing example, the equation will read: 

. 400(1,0586—1) 

^ 1.0586'"—1 


It has been stated in the preface that all solutions will be given by the 
Tables only ; consequently, the rate of 5.86% not existing in Table I, the nearest 
rate will be taken, i.e. 5% or 5.875%, the difference being comparatively small. 
Table I, page 43, shows thatl.05875^, or $1 invested at 5%% compound interest 
for 30 years, becomes $5.543729; therefore, the equation reads : 


. 400(1.08575—1) 

^ 5.543729—1 


=$5,172. 


By logarithms, using the exact rate of 5.86%, the result is $5,184, the difference 
being only 0.012%. 


Thus the annuity, which will amortize the premium, or the difference be¬ 
tween the purchase price and the redemption] value, being $5,184, by capitalizing 
this amount every year at 5.86% compound interest, the result will be equal to 
the $400 premium. 

Furthermore, if this amount $5,184 is added to the $30, the yearly interest 
the investor will receive annually $35,184 for every $600 invested, and this in¬ 
come represents exactly an investment at the income rate 5.86%. 


— o — o — o — 


PROBLEM. 

To determine the purchase price of a bond at a fixed income rate. This 
problem is plainly the reverse of the preceding one.* 

EXAMPLE —What price must be paid for a bond, which will be redeemed at 
$1,000 after 30 years, yielding annual interest of $30, if it is desired to obtain 
an income rate of 7 % ? 

The algebraic equation mentioned in the note, expressed in the figures of 
this problem will read: 

1000(1.07—1)+1000(1.03—1)(1.07^—1) . 70+30(1.07^—1) 

(1.07—1)(1.07“—1)+(1.07—1) 0.07(1.07^—1)+0.07 


♦MARGINAL NOTE—The following algebraic equation is applicable to this case. 

A c{q — l)-|~c(p — 1) {q^ 1) 

{q —1) (q”—l) + (q—1) 

-which has the same elements as the first one in this chapter, i.e. 
c=the par or redemption value of the bond. 
p=the unit plus its nominal rate of interest. 
n==the time. 

q=the unit plus the income rate of investment. 
a=the market price, or unknown quantity. 

51 










ANNUITIES AND AMORTIZATION TABLES 


Table I, page 47, shows that $1. invested @7% compound interest, for 30 
years, becomes $7.612266; therefore the equation reads: 


70+30X6.612266 

0.07X6.612266+0.07 


$503.63, 


the purchase price which will be paid at an income rate of 7%. 

DIRECT SOLUTION BY THE TABLES 


The same problem may be solved more easily by the Tables as follows: 

The investor will receive an annual income of $30 for 30 years, plus the re¬ 
demption value of the bond $1,000 at the end of the 30th year. Therefore the 
market price of the bond is the actual value of the annuity of $30, @7% com¬ 
pound discount, plus the actual [value of i$1000, payable after 30 years @7% 
compound discount. 

Table VI, page 217, shows that the actual value of an annuity of $1, pay¬ 
able for 30 years @ 7 % compound discount, is 12.4090344. For $30 it will be 
12.4090344 X30=$372.271. Also Table V, page 179, shows that the actual 
value of $1, payable after 30 years at 7% compound discount, is 0.1313669. For 
$1000 this will be 0.1313669 X1000=$131.3669. Consequently the addition of 
the two values is $372.271+$131.3669=$503.6379, which is the market price 
of the bond to net 7%, and exactly the same price found by the first algebraic 
method. 


— O-O-O-0-— 

CALCULATION OF PARITIES 

In the foregoing example one of the most important problems in financial 
transactions has been solved, Le. the calculation of Parities of securities. 

Parity means analogous, equivalent or equal. 

The next chapter will be devoted to Parities, but before closing this chapter 
it is desirable to show the importance of the calculations already made by using 
a practical illustration, viz. 

~ o — o — o •— 

PROBLEM. 

A man owns a bond of a known market price and rate of interest. He 
wishes to buy also another kind of a bond of a known rate of interest to net him 
an income rate equal to the first one. What price must he pay for the second 
bond ? 

EXAMPLE—An investor owns a bond which will be redeemed at $1200 
after 40 years, with interest coupons of $60 per annum, for which he paid the 
market price of $1000. What price must he pay for another bond, which will 
be redeemed at $1000 after 50 years, with interest coupons of $40 per annum, 
to net him the same rate, the security of principal being absolutely equal in both 
bonds ? 


52 





ANNUITIES AND AMORTIZATION TABLES 


The rate of the investment of the first bond must be found as follows: 

The following algebraic equation is applicable to this case. 

+1, See page 49, (previous). After trying dif¬ 
ferent rates we found that QVs is equal to q : 


1.06125''= 


200X0.06125 


1000 X 0.06125—1200 X 0.05 


+ 1 =- 


12.25 


1.25 


+ 1 = 10.8 


Table I, page 43, shows that the value of $1. invsted @6% compound in¬ 
terest for 40 years, is $10.28575, and @ is $11.30202; therefore according 
to proportion, @ it will be $10.79388. 

In this case the investment nets 6%%. 

To find the price that must be paid for the second bond, the equation will 
read: 


. 1000(1.06125—1)+1000(1.04—0)(1.06125^—1) 

(1.06125—1)(1.06125“—1)+(1.06125—1) * 

61.25+40 X (1.06125^—1) 

^ 0.06125(1.06125“—1)+0.06125 ’ 


61.25+40X18.57143 

^“0.06125X18.57143+0.06125 


=$670.80. 


This will be the price of the second bond to net an investment rate of 6^%. 


DIRECT SOLUTION BY THE TABLES 


The same problem may be solved more easily by the tables by discounting 
the annuities and the redemption value of the bond as follows: 

Table VI, page 213, shows that the actual value of an annuity of $1, payable 
for 50 years, @6% compound discount, is $15.7618. At it will be 

$15,503, determined by proportion, which is sufliciently close for this case. 
Therefore the actual value of 50 annuities of $40 each will be 

15.503X40=$620.12 

Also Table V, page 179, shows that the actual value of $1, payable after 
50 years, @6% compound discount, is 0.05428815; @ OYsfo it will be 0.051143, 
determined by proportion. 

Therefore the actual value of $1000 will be 0.051143 X1000=$51.14. 
Consequently the addition of the two actual values 

$620.12 

51.14 

$671.26 

is the market price of the bond, and very nearly the same result found by the 
first solution. 


53 











ANNUITIES AND AMORTIZATION TABLES 


Thus the investments to be at parity will read: 
1st investment Redemption price $1200. 


2nd 


» 


?> 


» 

» 


Years to run 40. 

Attached coupons of $60 each per annum. 
Market price $1000. 

The investment nets 6y8%. 

Redemption Price $100(3. 

Years to run 50. 

Attached coupons of $40 each per annum. 
The investment to net 6%%. 

The Market price must be $670.80. 


B.—WHEN THE REDEMPTION DATE IS NOT KNOWN 

There are two cases when the redemption date of a bond is not known. i.e, 

1st —When the bond is irredeemable, and will not be paid off, and will never 
mature. These interest-bearing, debt certificates are perpetual and exist forever. 
This class of bonds are always Government bonds; and if the Government 
wishes to retire them it must go into the open market and buy them at the mar¬ 
ket price. The best known examples of this class are the English and Egyptian 
“ Consols ”, and the French “ rente perpetuelle”, although of course the English 
Consols are not technically bonds. The French name is really correct, because 
it actually means perpetual income or income forever^ in distinction to the “ rente 
amortissable ”, i.e. the amortizable income, which term is applied to the other 
class of French Government bonds. 

In this class of bonds there is no question of amortization, par value, invest¬ 
ment rate, etc. The investment simply pays a perpetual income. Their value 
is the current market price. 

Mention must be made also that in transacting business in these bonds 
the capital is not generally mentioned, only the income, e.g. an investor in buy¬ 
ing on the Bourse of Paris 5000 fcs. perpetuelle, or on the London Stock Ex¬ 
change £200 of Consols “at 75”, means that he buys in Paris an income of 
5000 fcs., or in London an income of £200, at the rate of 21/2% income for every 
75 capital invested. In this case there is an investment of a nominal capital of 
200,000 fcs. having a market value of 150,000 fcs. the income rate being 3.33%; 
or in London, a nominal capital of £8000, having a market value of £6000, and 
an income rate of 3.33%. 

2nd —When the bonds are amortized, redeemed, or paid off by drawings an¬ 
nually, semi-annually, quarterly or monthly. In this case it is of special interest to 
the investor to know the income rate, as this vitally depends upon the likelihood 
of redemption, which may happen at any drawing. There is a great difference 
of opinion upon the solution of this problem, but the best method of solution 
may be that based upon the probable date of redemption. In an endeavor to 
determine this, there can be no certainty in the calculation, because the date of 
redemption by drawing may not coincide with this probable date. 


54 







ANNUITIES AND AMORTIZATION TABLES 


Notwithstanding this uncertamty the question is susceptible of a mathematical 
solution. Though the redemption date is unknown, it being determined for each 
bond by a drawing, nevertheless it must be arbitrarily fixed, for the purpose of the 
calculation, at such a point of time as will make the income rate received by the 
investor as if it were equal to the effective rate of the loan. The unknown 
date of redemption thus fixed is called the mathematical or average date of the 
bond. 

The effective or real rate of interest has been discussed in Chapter VI, but 
was not completed there. The exact difference between the income rate of the 
investment and the effective or real rate of interest of the loan must be estab¬ 
lished, because in many cases the two rates are identical, e. g .—When an indi¬ 
vidual or a corporation subscribes the total amount of a loan, the redemption 
date of which is not known in advance, the chances of redemption by drawings' 
will counterbalance one another so that ultimately the purchaser of the whole 
loan will receive an income rate on the investment equal to the effective rate of 
interest paid by the borrower. Furthermore, when a bond is bought at the rate 
of its issue, it is also clear that the investor receives an average rate of interest, 
on his investment equal to the real or effective rate of interest of the loan. 

But in the example of Chapter IV the investor in the bonds of the railroad 
company, notwithstanding that he bought [them at the price of the issue, i.e. 
$700, did not receive an investment rate equal to the real or effective rate of in¬ 
terest of the loan, which was demonstrated to be 4.6503%, but only 4.36%. 

The problem is, a bond of a par or redemption value of $1000, to be re¬ 
deemed by drawings on the amortization plan in 75 years, bearing interest cou¬ 
pons of $30 per annum, has been bought at the rate of issue of $700; what is 
the income rate of the investment that the purchaser receives, or what does it 
net the investor ? 

Solving this problem as demonstrated on page 49 by the tables, it is found 
that this rate is between 4.25% and 4.375%, and by logarithms is about 4.36^2%. 

The solution of this problem permits of two conclusions: /s/, the investor 

either considers the chances of redemption by drawings and makes an average 
income rate on his investment of 4.6503%, which is the real or effective rate of 
the loan; or 2nd, he does not consider the chances of redemption by drawings 
and operates upon the basis that he will keep the investment during the whole 
life of the loan, and will not cash the premium until the end of the 75th year, in 
which case his income rate is 4.36V2%. 


55 




ANNUITIES AND AMORTIZATION TABLES 


MATHEMATICAL DATE. 

Mention must be made again that the discussion is of loans redeemed on 
the amortization plan by drawings, and consequently the bonds may mature at 
any drawing; and the question is to find the date at which the bonds will be re¬ 
deemed when the investor receives an investment rate precisely equal to the 
real or effective rate of the loan.* 


By using the figures of the example, the algebraic equation of the note will 

1 1000(1.0465—D—1000(1.03—1) 46.5 —30 16.5 

'700(1.0465—D—1000(1.03—1) 32.55—30 2.55 

This 6.4706 is the amount to which $1. has increased after n years at 
4.65% compound interest. This rate does not exist in Table I, the nearest rate 
being 4%% or 4.625%, at which $1. will require 41 years to produce $6.383390; 
therefore n equals about 41 years, when the bond must be drawn. This is the 
mathematical date of the loan; and the investor has an income rate equal to the 
real or effective rate of interest of the loan. 


This manner of fixing the mathematical date of the maturity of the bond 
applies also when the investor buys his bonds at any time after their issue, with 
the understanding that the nominal price will be accounted from the date of the 
purchase. 

EXAMPLE:—An investor bought a bond of the above mentioned loan during 
the 26th year after its issue, the loan having only 50 years more to run. The 
amortization table of the loan, page 30, shows that with a capitalization rate of 
4.8581%, and a market price of $800 per $1000 par value, the real or effective 
rate is 4.252%. Therefore the algebraic equation will read: 

1000(1.0425—D—1000(1.03—1) 42.50—30 12.5 » 

1.U4ZD 800(1.0425—D—1000(1.03—1) 34—30 "" 4 * 


♦MARGINAL NOTE—The algebraic equation has the following elements: 

c=nominal or par value of the bond, in this case $1,000. 

a=real or market value of the bond, in this case 700. 

p=nominal rate of interest, in this case 5%. 

q=real or effective rate of interest 4.65% 

n = the number of years after the bond must be drawn to make the income rate of the in¬ 
vestment equal to the real or effective rate of interest of the loan, which in this case is the 
unknown quantity. 


Thus the mathematical date of redemption is represented by the equation. 


(c(p-l)) . . . . 1) 

By adding c, the par value to this equation It equals a real or market value, capitalized at 
the real interest q, for this same period, thus: 




therefore 


n c( q 1) — c( p —1) 

a{q —1)—c(/>—1) 


56 










ANNUITIES AND AMORTIZATION TABLES 


Table I. page 31, shows that $1. at 4^% will increase to about $3,125 in 
27 or 28 years; thus the bond must be drawn for redemption about the 27th 
year from the date of purchase, and the investor has therefore made an invest¬ 
ment which nets him the same income as the real or effective rate of interest of 
the loan. Therefore the mathematical date of this loan having no more than 50 
years to run, with a market value of the bonds at $800 will be between the 27th 
and 28th years. 


PROBABLE DATE 


In Chapter VI, the probable date of the redemption of a loan is defined as 
that date in the process of the redemption when the amount of the redeemed 
bonds is equal to the amount of those still outstanding. 

It is understood that it will not be right to base the calculation of the in¬ 
come rate on the probable date in solving the problem of how much the invest¬ 
ment nets, because the maturity of bonds redeemed by drawings may happen 
before or after the probable date. Furthermore, the probable date does not 
depend upon the market price of the bond; but the mathematical date depends 
upon it absolutely. 

A comparison of the probable date and the mathematical date will convince 
the reader and show the difference, which is as follows :* 


If the figures of the Example in chapter VI, page 30, replace the alge¬ 
braic equation mentioned in the note, the equation will read, 


1.03"= ""’0y°f°" +l=4.09+l==5.09 


Table I, page 20, column 3% shows that $1. @ 3% compound interest, 
becomes $5.082133 in 55 years, therefore the probable date is about 55 years. 
The Mathematical date has been solved as 41 years. 

The Probable date has been solved as 55 years. 

The investment rate according to the mathematical date has been solved as 
4.65%. If the investment rate were solved according to the probable date, 
which is not correct, it would be 4.52%. 


♦MARGINAL NOTE—The elements of the Algebraic equation of the note will read: 
a=annuity or annual investment, in this case $366,798. 
q=the unit plus its rate of interest, in this case 1.03. 
c=the capital, in this case the half of $100,000,000. 

n=the unknown, or the number of years at which an annuity or an annual investment of 
an equal amount will accumulate to a known amount. 

Thus the well known geometric progression will read: 

a-{-aq-\-aq^-\~aq^-\-aq^ . . . aq^ ^=c 

from which ^; and therefore J-i 

q —1 o 


5 


57 








ANNUITIES AND AMORTIZATION TABLES 


CHAPTER IX 

PARITIES BY THE REAL RATE OF INTEREST 
CONTENTS 

Basis of the real or effective rate of interest.—Problem. Find the more advan¬ 
tageous i^ivestment between two bonds, the loans being made on the amortiza¬ 
tion plan.—Example.—Solution by the tables.—Problem. What must be the 
market price of a bond to be in parity with another bond ?—Example.—Differ¬ 
ence in the approximation by the calculation of proportion.—Problem. How to 
determine the parity of two bonds of different classes.—Example. French Rente 
perpetuelle and United States Liberty Loan. 

To solve the calculations of Parities, the real or effective rate of interest 
must be taken as a basis, because as has been demonstrated in the foregoing 
chapter, the basis of the net rate of the investment applies only when the re¬ 
demption date is known; but in many cases, and especially when the loan is is¬ 
sued on the amortization plan, the redemption date may not be known. 

The following problems will cover the field of parities in American and 
European finances. 

— o — o — o- 

PROBLEM. 

Which is the more advantageous investment between two bonds, when 
the respective loans are made on the amortization plan, and when their market 
price, their face or redemption value, the time of the loans, and their rate of 
interest are known, the security of the principal of both bonds being equal? 

EXAMPLE :—1st bond—Face value $1000, market price $720, annual inter¬ 
est coupon $30, to be redeemed in 65 years on the amortization plan. 

2nd bond—Face value $1000, market price $900, annual interest coupon 
$40, to be redeemed in 75 years on the amortization plan. 

Which investment is the more advantageous ? 

SOLUTION BY THE TABLES. 

1st bond—The real or effective rate of interest must be determined as 
follows: 

Table III, page 112, shows that the annuity, which will amortize a capital 
of $1 @ 3% in 65 years on the amortization plan, is: 0.03514584; therefore 
for $1000 nominal capital it will be 0.03514584X1000=35.14584. But in this 
case the face value of the bond is $1000, and the market price is $720; there¬ 
fore the capitalization rate will be 35.14584-^720=0.04881366 per $1. This 
capitalization rate corresponds in the line of 65 years, Table III, page 116, to a 
real rate of interest between 4y2 and4%%. 


58 




ANNUITIES AND AMORTIZATION TABLES 


Furthermore, by the calculation of proportion, as demonstrated on page 49, 
which is not absolutely exact, but which permits a closer approximation, it was 
found that when the capitalization rate augments 

0.04994621—0.04773047=0.00221574, the real rate of interest 
augments 4 % —4y2%=i/4 % ; therefore when the capitalization rate augments 
0.04881366—0.004773047=0.00108319, the real rate of interest will augment 
0.00108319X0.25-^0.00221574=0.122215. Therefore the real rate of interest 
is: 4.5-f0.122215=4.622215%. 

2nd bond—In making the same calculation as for the first bond, it is found 
that the capitalization rate is 0.04692113 per $1, which corresponds to the real 
rate of interest of 4.521862%. Therefore the first investment is more advan¬ 
tageous than the second. 

-0 — 0— o — o — 

PROBLEM. 

ViThat must be the market price of a bond to be in parity with another 
bond; or what must be the market price of a bond, of which the investment rate 
will be equivalent to that of another bond ? 

EXAMPLE:—1st bond—Pace value $1000, market price $720, annual in¬ 
terest coupon $30, to be redeemed in 65 years on the amortization plan. 

2nd bond—Face value $1000, annual interest coupon $40, to be redeemed 
in 75 years on the amortization plan. 

What must be the market price of the second bond to be in parity with the 
first; or what must be the price of the second bond to yield an investment rate 
equal to the first one ? 

The rate that the first investment nets is known from the foregoing as 
4.622215%. Therefore the capitalization rate, or the annuity which will amor¬ 
tize a capital of $1. @ 4.622215% in 75 years on the amortization plan, must be 
found. This rate of interest of 4.622215% does not exist in the tables, but is 
between 41^% and 4%% ; therefore the annuity or capitalization rate for each 
of these rates is 0.04672104 and 0.04900913 per $1. respectively. By the cal¬ 
culation of proportion, notwithstanding that this calculation is not absolutely 
exact, although it has several decimals, and gives an almost exact result, it is 
found that when the rate of interest diminishes 0.25 (4.75—4.50) the annuity 
will diminish 0.00228809 per $1, (0.04900913—0.04672104=0.00228809). 
Therefore the augmentation of the interest being: 4.622215—4.50=0.122215, 
that of the annuity or capitalization rate wiU be: 

0.122215X0.00228809^0.25=0.00111855. 

Therefore by adding 0.00111855 to 0.04672104, it equals 0.04783959, which is 
the annuity that will amortize a capital of $1. at the real rate of interest of 
4.622215%. But according to table III, page 116, the annuity which will amor¬ 
tize a capital of $1. @ 4% in 75 years is 0.04222902; therefore the real capital 
which will be amortized by an annuity of 0.04783959 will be 
0.04222902-5-0.04783959=0.8827211. 

Therefore the real capital or the purchase price of the $1000 bond will be 
0.8827211 X1000=$882.7211 
59 




ANNUITIES AND AMORTIZATION TABLES 


to be in parity with the first bond; and at a market price of $882.72 the second 
bond will net the purchaser 4.6222159^. 

DIFFERENCE IN THE APPROXIMATION BY THE CALCULATION 
OF PROPORTION. 

It has been admitted in the foregoing, that the calculation by proportion is 
not absolutely exact; but the tables having several decimals give an almost 
exact result. The following calculation will show what the error actually is. 

The difference between the two annuities of 0.04900913 and 0.04672104 is 
0.00228809; and they represent rates of 4%% and 4^2% respectively for 75 
years. The difference between two annuities, which for the same time represent 
rates of 5% and 4y2% is: 0.05132162—0.04672104=0.00460058. When the 
difference is 0.00228809, the rate of interest augments by or 0.25%. 
When the difference is 0.00460058, what will be the augmentation of the rate 
of interest ? This question stated in the form of a p roportion will give the fol¬ 
lowing result: 0.00228809 : 0.00460058=0.25 : x; or 

x=0.00460058 X 0.25^0.00228809=0.5026. 

Adding 0.5026 to 4 ^ 2 % equals 5.0026%; therefore the error is only 0.0026%. 

—.0 — 0 — o — o — 

PROBLEM 

How to determine the parity of two bonds of different classes, the one re¬ 
deemable at a fixed redemption date, and the other not redeemable, but perpetual. 

EXAMPLE —To determine the parity of the 4% Liberty Loan of the United 
States, at par in 20 years, with the 3% French rente perpetuelle at a market 
price of 66.50 fcs. 

In this case the foreign exchange will be considered at 5 fcs. to $1. A 
perpetual Government bond must be considered as having an investment rate 
equal to the rate at which it is purchased. Therefore the 3% French rente 
perpetuelle constitutes an investment of: 

3X100-^66.50=4.511% 

To find the parity of the 4% Liberty Loan, it must be found at what price 
the latter will also constitute an investment at the rate of 4.511%. This rate 
is not in the Tables; therefore the rate of 4.50% will be considered, as the 
difference of 0.011% is quite inappreciable. 

The solution is made as on page 52, Chapter VIII, by discounting the 
annuities and adding the actual value of the capital. 

Table VII, page 235, shows that the actual value of 40 semi-annuities of $1. 
@ 4y2% per annum, is 26.1935498; therefore for 40 semi-annuities of $2. each 
it will be: 26.1935498X2=$52.3870996. 

Also Table V, page 170, shows that the actual value of an amount of $1. 
after 20 years @ 4y2% compound discount, is 0.4146427; therefore for $100. it 
will be: 0.4146427X100=$41.46427. 

Therefore the 4% United States Liberty Loan, to be in parity with the 3% 
French rente perpetuelle at fcs. 66.50, must be bought at 
$52.3870996-f-$41.46427=$93.85. 


60 




ANNUITIES AND AMORTIZATION TABLES 


CHAPTER X 

FARM LOANS 

EXTRACTS FROM THE FEDERAL FARM LOAN ACT 
CONTENTS 

Extracts from the Federal Farm Loan Act.—Method of procedure in 
obtaining farm loans.—Problem. Find the Annuity.—Tabular Illustration— 
Semi-annuity.—Tabular Illustration.—Problem. Find the period of time. 
—Problem. Find the rate of interest.—Problem. Find the remaining capital 
due after a payment of a number of annuities.—Problem. Find the new annuity 
after a partial, anticipated payment.—Farm Loan Bonds.—Elasticity for ex¬ 
pansion and contraction of credit to the farmers. 

— o — o — o — o- 

The foundation of really the first extensive and efficient system of Agri¬ 
cultural Banking in the United States under Federal direction and control, en¬ 
dowed with unlimited resources to meet any requirements that may eventuate 
through the future growth of the plan, has been the institution of the Farm 
Loan Board, Federal Land Banks, National Farm Loan Associations and Joint 
Stock Land Banks, which have been created by the Federal Farm Loan Act of 
July 17, 1916. 

The Federal farm loan act was designed to provide capital for ag¬ 
ricultural development, to create standard forms of investment based upon farm 
mortgages, to equalize rates of interest upon farm loans, to furnish a market 
for United States bonds, and to create Government depositaries and financial 
agents for the United States. 

FEDERAL FARM LOAN BOARD 

The Federal Farm Loan Board consists of five members, including the 
Secretary of the Treasury, who is a member and chairman ex-officio. 

The purpose and powers granted by the Act are as follows: 

ht —To divide the continental United States, excluding Alaska, into twelve 
districts, and organize, charter, and establish a Federal Land Bank in each 
district, and to charter National Farm Loan Associations, and Joint Stock 
Land Banks. 

2nJ —To appoint a farm loan registrar, land bank appraisers, and land 
bank examiners in each district. 

JrJ—To receive applications for issues of farm loan bonds. 

4th —To review and alter the rate of interest to be charged by Federal 
Land Banks. 

5th —To make rules and regulations respecting the charges made to bor¬ 
rowers on loans for expenses of appraisal, determination of title, and recording 
of same. 


61 





ANNUITIES AND AMORTIZATION TABLES 


6th —To exercise general supervisory authority over the Federal Land 
Banks, the National Farm Loan Associations, and the Joint Stock Land Banks. 

FEDERAL LAND BANKS 

The capital stock of every Federal Land Bank shall be not less than 
$750,000 and shall be divided into shares of $5. each. 

All Federal Land Banks, when designated for that purpose by the Secre¬ 
tary of the Treasury, shall be depositaries of public funds. 

All Federal Land Banks shall issue and sell farm loan bonds, subject to the 
approval of the Federal Farm Loan Board. 

The Federal Land Banks shall invest their funds in qualified first mort¬ 
gages on farm lands. 

They shall acquire and dispose of real or personal property. 

NATIONAL FARM LOAN ASSOCIATIONS 

All persons desiring to borrow money on farm mortgage security may 
organize a National Farm Loan Association. 

The shares in National Farm Loan Associations shall be of the par value 
of $5. each. 

The National Farm Loan Associations shall have power to indorse mort¬ 
gages, taken from their shareholders, to the Federal Land Bank. 

To issue certificates against deposits of funds, bearing interest not to ex¬ 
ceed four per cent, per annum, and for not longer than one year, convertible 
into farm loan bonds when presented at the Federal Land Bank. 

METHOD OP PROCEDURE IN OBTAINING FARM LOANS. 

Whenever any person desires to secure a loan on a first mortgage he shall 
proceed as follows: 

/ st —^Make application for membership to the National Farm Loan Associ¬ 
ation of his district, stating the amount of the desired loan, and subscribing for 
capital stock of the National Farm Loan Association to the extent of five per 
cent, of the loan, the subscription to be paid in cash upon the granting of the 
loan. 

2nd —The application for membership and for a mortgage loan shall be 
first referred to the loan committee of the National Farm Loan Association, 
who shall examine the land offered as security, and shall make a detailed written 
report, giving the appraisal of the land and such other information as may be 
required. 

Srd —All loans shall be made for the following purposes and under the fol¬ 
lowing terms and conditions: 

(a)—To provide for the purchase of land for agricultural uses. 

(h)—To provide for the purchase of equipment, fertilizers and live stock. 

(c) —^To provide buildings and for the improvement of farm lands. 

(d) —To liquidate indebtedness of the owner of the land mortgaged. 

62 





ANNUITIES AND AMORTIZATION TABLES 


(e)—No such loan shall exceed fifty per cent, of the value of the land 
mortgaged, and twenty per cent, of the value of the permanent insured improve¬ 
ments thereon, said value to be ascertained by appraisal. 

(/)—The amount of loans to any one borrower, shall in no case exceed a 
maximum of $10,000, nor shall any loan be for a less sum than $100. 

4th —The written report of the loan committee of the Association shall 
be submitted to the Federal Land Bank, together with the application for the 
loan, which shall be referred to the appraiser, who shall investigate and make a 
written report upon the land. 

5ih —If the appraiser’s written report is favorable and the loan is granted, 
the Association shall subscribe for capital stock of the Federal Land Bank to 
the amount of five per cent, of the loan, the subscription to be paid in cash upon 
the granting of the loan. 

6th —The loans shall be secured by duly recorded first mortgages on farm 
land, within the land bank district. 

7th —Every such mortgage shall contain an agreement, providing for the 
repayment of the loan on the amortization plan, by means of a fixed annuity or 
semi-annuity covering; first, a charge on the loan; second, a charge for admin¬ 
istration and profits at a rate not exceeding 1 % per annum, said two rates 
combined constituting the interest rate on the mortgage; and, third, such 
amounts to be applied on the principal as will amortize or extinguish the debt 
within an agreed period of not less than five years, nor more than forty years. 

— o — o — o- 

PROBLEM. 

Knowing the borrowed capital, the rate of interest and the period of time, 
find the annuity, or the amount of interest and the proportion of the capital that 
must be paid annually or semi-annually, to amortize the borrowed capital during 
the fixed period of time. 

EXAMPLE A —A farmer, through the Farm Loan Association of which he 
is a member, borrows from the Federal Land Bank of his district $4000. @5% 
interest per annum, the loan to be redeemed in 20 years by 20 equal annual in¬ 
stalments. 

SOLUTION.—Table III, page 118, shows that the annuity of $1. for 20 years 
@ 5% is 0.08024255; therefore the annuity of $4000, will be: 

0.08024255 X4000=$320.9702, 
which for the first year will be divided as follows: 

$200 interest, 

120.9702 amortization quota of the capital. 

$320.9702 Total annuity. This, of course, will vary in detail each succeeding 
year, but will be the same in the aggregate each year. 

To compute the amortization table of this loan, the method is as follows: 

63 





ANNUITIES AND AMORTIZATION TABLES 


ID 

D 

D1 

(M 

X ID 

X 

Tf p 

rH 05 

d d 

d d 

CD X 

ISO (N 

X 

X 


o 

00 

O CD 

a rH 

CP 00 
IQ CO 


O 

00 

CD l> 

o a 
i6 d 
Oi (M 
•t—( CO 


ID 

o a 
t- o 

CO 

t- 

X 


ID 

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173.9305 133.3160 81.4680 15.2835 

3478.61 2666.12 1629.16 305.69 

3652.54 2799.4360 1710.6280 320.97 

320.97 X 320.97 XV 320.97 XX 320.97 

3331.57 2478.46 1389.65 0 
































































ANNUITIES AND AMORTIZATION TABLES 


With the aid of these figures, which show the exactitude of the solution, 
the following table shows for the end of every year the outstanding capital, the 
annuity, the interest and the amortization quota, or the portion of the capital 
paid ever}) year to extinguish, at the end of 20 years, the whole loan. 


Outst’nd’g 

Total ( 

1 Which is divided into ') 

Outst’ndV 

Years Capital -f- Interest = 

Amount — Annuity < 

Interest-(-Amortizat’n > 

• Capital at 

at the beginning 

Due i 

t quota ) 

the end of 

of every year 



each year 


1 

4,000.00 

200.00 

4,200.00 

320.97 

200.00 

120.97 

3,879.03 

2 

3,879.03 

193.95 

4,072.98 


193.95 

127.02 

3,752.01 

3 

3,752.01 

187.60 

3,939.61 


187.60 

133.37 

3,618.64 

4 

3,618.64 

180.94 

3,799.58 


180.94 

140.03 

3,478.61 

5 

3,478.61 

173.93 

3,652.54 


173.93 

147.04 

3,331.57 

6 

3,331.57 

166.58 

3,498.15 

320.97 

166.58 

154.39 

3,177.18 

7 

3,177.18 

158.86 

3.336.04 


158.86 

162.11 

3,015.07 

8 

3,015.07 

150.75 

3,165.82 


150.75 

170.22 

2,844.85 

9 

2,844.85 

142.24 

2,987.09 


142.24 

178.73 

2,666.12 

10 

2,666.12 

133.31 

2,799.43 


133.31 

187.66 

2,478.46 

11 

2,478.46 

123.93 

2,602.39 

320.97 

123.93 

197.04 

2,281.42 

12 

2,281.42 

114.07 

2,395.49 


114.07 

206.90 

2,074.52 

13 

2,074.52 

103.72 

2,178.24 


103.72 

217.25 

1,857.27 

14 

1,857.27 

92.86 

1,950.13 


92.86 

228.11 

1,629.16 

15 

1,629.16 

81.46 

1,710.62 


81.46 

239.51 

1,389.65 

16 

1,389.65 

69.48 

1,459.13 

320.97 

69.48 

251.49 

1,138.16 

17 

1,138.16 

56.90 

1,195.06 


56.90 

264.07 

874.09 

18 

874.09 

43.70 

917.79 


43.70 

277.27 

596.82 

19 

596.82 

29.84 

626.66 


29.84 

291.13 

305.69 

20 

305.09 

15.28 

320.97 


15.28 

305.69 




2,419.40 


6,419.40= 

=2,419.40+4,000.00 



EXAMPLE B —A farmer, through the Farm Loan Association of which he is. 
a member, borrows from the Federal Land Bank of his district $4000 @5% 
interest, the loan to be redeemed in 20 years, by 40 equal, semi-annual instal¬ 


ments. 

Table IV, page 149, shows that the semi-annuity of $1. for 20 years @ 5%, 
is 0.03983616; therefore the semi-annuity of $4000 will be: 

0.03983616 X4000=$159.34464. 

The first year, the first and second instalments will be divided as follows: 
First instalment. 

$100. interest 

59.34464 amortization quota of the capital 
$159.34464 Total first year’s, first semi-annual instalment. 

Second instalment. 

$98.51638 interest 

60.82826 amortization quota of the capital 
$159.34464 Total first year’s, second semi-annual instalment. 

65 










ANNUITIES AND AMORTIZATION TABLES 


Years 

Semi- 

unual 

insUkl- 

menU 

Outstanding 
Capital -4- 

at the beginning 
of every year 

Interest 

= Total — 

Semi- 

Annuity 

( Which is divided into 
■J amortization 

( Interest quota 

1 

1st 

4000. 

100. 

4100. 

159.3446 

100. 

59.3446 


2nd 

3940.6554 

98.5163 

4039.1717 


98.5163 

60.8283 

2 

3rd 

3879.8271 

96.9957 

3976.8228 


96.9957 

62.3489 


4th 

3817.4782 

95.4370 

3912.9152 


95.4370 

63.9076 

3 

5th 

3753.5706 

93.8392 

3847.4098 


93.8392 

65.5054 


6th 

3688.0652 

92.2017 

3780.2669 

159.3446 

92.2017 

67.1429 

4 

7th 

3620.9223 

90.5230 

3711.4453 


90.5230 

68.8216 


8th 

3552.1007 

88.8025 

3640.9032 


88.8025 

70.5421 

5 

9th 

3481.5586 

87.0390 

3568.5976 


87.0390 

72.3056 


10th 

3409.2530 

85.2313 

3494.4843 


85.2313 

74.1133 

6 

11th 

3335.1397 

83.3784 

3418.5181 

159.3446 

83,3784 

75.9662 


12th 

3259.1735 

81.4793 

3340.6528 


81.4793 

77.8653 

7 

13th 

3181.3082 

79.5327 

3260.8409 


79.5327 

79.8119 


14th 

3101.4963 

77.5374 

3179.0337 


77.5374 

81.8072 

8 

15th 

3019.6891 

75.4922 

3095.1813 


75.4922 

83.8524 


16th 

2935.8367 

73.3959 

3009.2326 

159.3446 

73.3959 

85.9487 

9 

17th 

2849.8880 

71.2472 

2921,1352 


71.2472 

88.0974 


18th 

2761.7906 

69.0447 

2830.8353 


69.0447 

90.2999 

10 

19th 

2671.4907 

66.7872 

2738.2779 


66.7872 

92.5574 


20th 

2578.9333 

64.4733 

2643.4066 


64.4733 

94.8713 

11 

21st 

2484.0620 

62.1015 

2546.1635 

159.3446 

62.1015 

97.2431 


22nd 

2386.8189 

59.6704 

2446.4893 


59.6704 

99.6742 

12 

23rd 

2287.1447 

57.1786 

2344.3233 


57.1786 

102.1660 


24th 

2184.9787 

54.6246 

2239.6033 


54.6246 

104.7200 

13 

25th 

2080.2587 

52.0065 

2132.2652 


52.0065 

107.3381 


26th 

1972.9206 

49.3230 

2022.2436 

159.3446 

49.3230 

110.0216 

14 

27th 

1862.8990 

46.5725 

1909.4715 


46.5725 

112.7721 


28th 

1750.1269 

43.7532 

1973.8801 


43.7532 

115.5914 

15 

29th 

1634.5355 

40.8634 

1675.3989 


40.8634 

118.4812 


30th 

1516.0543 

37.9014 

1553.9557 


37.9014 

121.4432 

16 

31st 

1394.6111 

34.8653 

1429.4764 

159.3446 

34.8653 

124.4793 


32nd 

1270.1318 

31.7533 

1301.8851 


31.7533 

127.5913 

17 

33rd 

1142.5405 

28.5635 

1171.1040 


28.5635 

130.7811 


34th 

1011.7594 

25.2940 

1037.0534 


25.2940 

134.0506 

18 

35th 

877.7088 

21.9427 

899.6515 


21.9427 

137.4019 


36th 

740.3069 

18.5077 

758.8146 

159.3446 

18.5077 

140.8369 

19 

37th 

599.4700 

14.9868 

614.4568 


14.9868 

144.3578 


38th 

455.1122 

11.3778 

466.5000 


11.3778 

147.9668 

20 

39th 

307.1554 

7.6789 

314.8343 


7.6789 

151.6657 


40th 

155.4897 

3.8872 

159.3769 


3.8872 

155.4574 


0.0323 2373.8063 6373.7840 2373.8063 3999.9777 

6373.7840 


66 









ANNUITIES AND AMORTIZATION TABLES 


It will be remarked that the semi-annual instalment is the same in the 
aggregate each half yearly period, but varies in detail, always diminishing in 
the interest and increasing in the amortization quota. 

To compute the amortization table and the table showing for the end of 
every six months the outstanding capital, the annuity, the interest and the 
amortization quota, or portion of the capital which must be paid every six 
months to extinguish, at the end of the 20th year, the whole loan, the process 
is practically the same as in the first example, with the exception that the in¬ 
terest is compounded and added to the capital every six months. 

For Semi-annual JImortization Table see page 66 (previous.) 

Remark—From the foregoing it should be noticed that the addition of two 
semi-annual instalments is not equal to one yearly annuity but slightly smaller, 
notwithstanding there is the same capital, same rate of interest and same 
length of time. The reason is, that the periods, for which the amortization 
quotas are reckoned, are more frequent. Furthermore, all the annuities and 
amortization problems are based on compound interest, which is added to the 
capital at the end of each period, producing a new basis for the interest. There¬ 
fore all semi-annual problems must be solved by Tables IV and VII. 

-O T- o — o- 

PROBLEM 

Knowing the annuity or the necessary amount to amortize a borrowed cap¬ 
ital, the rate of interest, and the period of time, find the capital that may be 
borrowed. 

EXAMPLE —^What capital may a farmer borrow @ 5% per annum, when 
he is able to use $320.97 of his income as annuity for 20 years ? 

Table III, page 118, shows that to amortize a capital of $1. @ 5% in 20 
years, the annuity is 0.08024255; therefore with an annuity of $320.97 the 
capital which will be amortized will be 320.97-^-0.08024255=$4000. 

This problem may also be solved more easily by Table VI. 

Table VI, page 208, shows that the actual value of an annuity of $1. for 20 
years @ 5% is $12.4622099; therefore the actual value of an annuity of 
$320.9702 will be 12.4622099X320.9702=3999.99800, which in reality is $4000. 

— o — o — o — 

PROBLEM 

Knowing the borrowed capital, the annuity and the rate of interest, find 
the period of time. 

EXAMPLE —For how many years must a farmer pay an annuity of $320.97 
to amortize a capital of $4000, @ 5% compound interest? 

The annuity of $4000, being $320.9702, the annuity of $1. will be 
$320.9702-^-4000=0.08024255. 

Table III, page 118, shows that the annuity of $1. @ 5% is 0.08024255 in 
the line of 20 years, which is the length of time applying to this example. 

In practice this exactness does not always follow. Therefore see page 20, 
Chapter III. 


67 




ANNUITIES AND AMORTIZATION TABLES 


PROBLEM 

Knowing the borrowed capital, the annuity and the period of time, find the 
rate of interest. 

Example —At what rate of interest may a farmer borrow $4000, paying 
an annuity of $320.9702 for 20 years to amortize his debt ? 

First, the annuity of $1. must be found as follows: 

The annuity of $4000 being $320.9702, the annuity of $1. will be 
320 . 9702 -^- 4000 = 0 . 08024255 . 

Table III, page 118, line of 20 years shows that this annuity for $1. of 
0.08024255 corresponds to a rate of 5% per annum. 

If the rate of interest cannot be found exactly with the tables, a proced¬ 
ure similar to that for the length of time must be used, see page 20, Chapter III. 

SEMI-ANNUAL INSTALMENT 

The foregoing problems have been solved with the understanding that the 
annuity is paid yearly, at the end of each year, which for the farmer is generally 
at the end of his harvesting season; but in practice very often, as the Farm 
Loan Act also permits, the annuity may be payable in two semi-annual instal¬ 
ments. Therefore the problems must be solved by Tables IV and VII, instead of 
Tables III and VI respectively. 

For the purpose of facilitating the work of the Farm Loan Board, Federal 
Land Banks, National Farm Loan Associations, Joint Stock Land Banks and 
others, besides giving a broader use for the Tables, the following problems 
which are found very often in daily practice are added here. 

—0—0—o—o— 

PROBLEM 

Knowing the borrowed capital, the annuity, the period of time and the rate 
of interest, find the amount of the remaining capital due after a payment of a 
number of annuities. 

EXAMPLE—Find what is the remaining capital after a payment of six 
annuities of $320.9702 each, the loan being made for 20 years @ 5% on $4000 
capital. 

SOLUTION A —Divide the annuity of the loan by the annuity of $1. for the 
remaining length of time. 

The annuity of $1. for the remaining 14 years is 0.1010240, found in Table ■ 
III, page 118, column 5%, line of 14 years; therefore 
320.9702-f-0.1010240=$3177.18. 

This is the amount computed in the amortization table of the loan, page 65. 

SOLUTION B —This problem also may be solved more easily by Table VI, 
where page 208, shows that the actual value of an annuity of $1. for 14 years, 
the remaining time, @5% per annum, is 9.8986407; therefore the actual value 
of an annuity of $320.9702 will be 9.8986407 X320.9702=$3177.17868. 


68 




ANNUITIES AND AMORTIZATION TABLES 


PROBLEM. 

Knowing the borrowed capital, the annuity, the length of time and the 
rate of interest, find the new annuity after a partial, anticipated payment. 

Example—W hat will be the new annuity of the loan, the farmer having 
made a cash payment of $1000 of the capital at the end of the sixth year, con¬ 
sidering that six annuities have been paid ? 

^ SOLUTION—Deduct the partial, anticipated payment from the remaining 
capital due, then multiply the remainder by the annuity of $1. corresponding to 
the remaining length of time and at the same rate of interest. 

In the previous example, the outstanding capital after a payment of six 
annuities, is - - $3,177.18 

deduct the cash payment of 1,000.00 
Amount due $2,177.18 

Multiply $2177.18 by 0:101024, the annuity of $1. for 14 years @ 5%, and 
the result is $219.94742, which is the new annuity. 

Another method of solving this problem is: deduct from the present annuity 
the annuity of the partial cash payment for the remaining length of time, at 
the same rate of interest. 

The present annuity is - - - - $320.9702 

The annuity of the partial payment is 1000X0.101024= 101.0240 

Remaining annuity $219.9462 

Only 8 decimal places have been considered for the making of these tables, 
consequently, a difference of one tenth of one cent or less cannot be taken into 
consideration. 

—o—o—o—o— 

EXTRACT FROM THE FEDERAL FARM LOAN ACT ON FARM LOAN 

BONDS. 

Federal or Joint Stock Farm Loan Bonds are secured by collateral deposited 
with a Farm Loan Registrar. 

Issue of bonds. 

When a Federal Land Bank makes application to the Federal Farm 
Loan Board for an issue of farm loan bonds, it must tender with the application 
as collateral security first mortgages on farm lands or United States Government 
bonds, not less in the aggregate amount than that of the bonds proposed to be 
issued. 

All first mortgages, or United States Government bonds will be transferred 
by assignment in trust to the Registrar for the district, to be held by him as 
collateral security for the farm loan bonds. 

The capital stock of a Federal Land Bank shall not be reduced to an 
amount less than 5% of the principal of the outstanding farm loan bonds 
issued by it. 

The bonds shall be issued in denominations of $25, $50, $100, $500 and $1000. 

They shall have coupons attached, payable semi-annually, and shall bear a 
rate of interest not to exceed 5% per annum. They may be exchanged for 
registered bonds of equal amount, and re-exchanged for coupon bonds, at the 
option of the holder. 


69 








ANNUITIES AND AMORTIZATION TABLES 


They are not taxable by National, State, Municipal or local authority. 

It may be readily surmised also from the foregoing, that the security of the 
bonds issued by the Federal Land Banks, having as collateral first mortgages 
on carefully appraised farm lands really increases in value every year. 

When the farmer pays his annual or semi-annual instalment, covering the 
interest and the amortization quota, he thereby reduces his loan yearly, and by 
this reduction of the loan automatically increases the value of the collateral 
security of the mortgage. 

Example —The above mentioned farmer, who borrowed $4000, @ 5%, to 
amortize his loan in 20 years by an annuity of $320.9702, pledged his farm as 
security for the loan. At the end of the sixth year he owes only $3177.18, with 
a collateral security of the same farm on which he borrowed originally $4000; 
likewise also in the 19th year he owes only $305.69 on a security, which 19 years 
before had been appraised good for a loan of $4000, and which furthermore has 
been continually developed in quality and value by the improvements that have 
been made, in buildings, amelioration of the land, drainage or irrigation. These 
have not been acquired for the benefit, or in the interest of the Farm Loan 
Association, or the Federal Land Banks, but for the farmer’s own benefit and 
betterment of all his surroundings and conditions. 

— o — o — o- 

ELASTICITY FOR EXPANSION AND CONTRACTION OF CREDIT TO FARMERS 

It is plainly evident from the Federal Farm Loan Act that the credit 
capacity of the system has the unique advantage of expanding and contracting 
credit to the farmers according to their needs. 

EXPANSION 

There are twelve Land Banks with $750,000 capital each, and according to 
the Act each Land Bank may borrow by issuing bonds, twenty times its capital, 
f.e. $15,000,000 secured by first mortgages on farm lands, and indorsed by the 
National Farm Loan Associations. Furthermore each Association in securing 
a loan from the Land Bank for one of its members is required to subscribe to 
the capital stock of the Land Bank an amount equal to 5% of the secured loan; 
therefore the automatic increase of the capital stock of the Land Banks pro¬ 
cures the automatic credit expansion of the Land Bank as follows: 

Capital of a Land Bank $750,000. 

Bonds issued on first mortgages 20 times the capital, $15,000,000. 

New capital subscribed at 5% of the loans on $15,000,000, $750,000. 

New bonds issued 20 times the new capital, $15,000,000. 

Therefore there is no limit to the expansion of credit for the ultimate 
benefit and use of the farmers. 

CONTRACTION 

The contraction of credit also results automatically, because the Land 
Banks are required to pay off the Farm Loan bonds whenever they mature, and 
to purchase them at par or below par from the funds of the amortization quotas, 
and other payments made on the principal of the first mortgages, 

70 





TABULAR 

SECTION 







TABLE I 


COMPOUND INTEREST 

S=CQ" 


The value of $1 invested for one to one hundred years at the following 
rates of compound interest. 


¥4% 

%% 

%% 

1 % 

IVs^o 

1^4% 

1 %% 

11/2% 

1%% 

1%% 

1%% 

2 % 

2Vs<!o 

21/4% 

2%% 

2%% 

2%% 

2%% 

2V8<ro 

3 % 


31/4% 

3%% 

SV2‘!o 

3%% 

3%% 

mTh 

4 % 



4%% 

41/4% 

4%% 

4%% 

4%% 

5 % 

5 %% 

SVi^lo 

5 %% 

5 %% 

5 %% 



6 % 

6 %% 

61/4% 


7 % 

7Vi% 

71/2% 


8 % 


8V2<ro 

8 %% 

9 % 

m°io 

m<ro 

d%‘/o 

10 % 


EXAMPLE—^What amount will accrue after 66 years, investing a capital of 
of $1000 @ per annum compound interest? 

C=$1000 <7=1.0875 n=66. 

5=1000X1.0875®® 

Table I, page 56, shows that <7^=1.0875®® or $1 invested for 66 years @ 
per annum compound interest becomes $253.7078. Therefore, 

5=1000 X253.7078=$253,707.80. 


6 


1 





Rate, to \% 
Years, 1 to 25 


TABLE I 

COMPOUND INTEREST 


The value of $1 invested at a fixed rate of compound interest for one 
to one hundred years. 


Years 

%% 

14% 

%% 

1% 

1 

1.002500 

1.005000 

1.007500 

1.010000 

2 

1.005006 

1.010025 

1.015056 

1.020100 

3 

1.007519 

1.015075 

1.022669 

1.030301 

4 

1.010038 

1.020151 

1.030339 

1.040604 

5 

1.012563 

1.025252 

1.038067 

1.051010 

6 

1.015094 

1.030378 

1.045852 

1.061520 

7 

1.017632 

1.035530 

1.053696 

1.072135 

8 

1.020176 

1.040708 

1.061598 

1.082857 

9 

1.022726 

1.045912 

1.069560 

1.093685 

10 

1.025284 

1.051141 

1.077584 

1.104622 

11 

1.027847 

1.056397 

1.085666 

1.115669 

12 

1.030417 

1.061679 

1.093808 

1.126825 

13 

1.032993 

1.066987 

1.102012 

1.138094 

14 

1.035575 

1.072322 

1.110277 

1.149475 

15 

1.038164 

1.077684 

1.118604 

1.160970 

16 

1.040759 

1.083072 

1.126994 

1.172580 

17 

1.043361 

1.088488 

1.135446 

1.184305 

18 

1.045969 

1.093930 

1.143962 

1.196148 

19 

1.048584 

1.099400 

1.152542 

1.208110 

20 

1.051206 

1.104897 

1.161186 

1.220191 

21 

1.053834 

1.110422 

1.169895 

1.232393 

22 

1.056469 

1.115974 

1.178669 

1.244717 

23 

1.059110 

1.121554 

1.187509 

1.257164 

24. 

1.061758 

1.127162 

1.1*96416 

1.269736 

25 

1.064412 

1.132798 

1.205389 

1.282433 


2 





TABLE I 


Rate, ViX to 1% 
Years, 26 to 50 


COMPOUND INTEREST 


The value of $1 invested at a fixed rate 
to one hundred years. 

of compound 

interest for one 

Years 

%% 

%% 

%% 

1% 

26 

1.067073 

1.138462 

1.214430 

1.295258 

27 

1.069741 

1.144154 

1.223538 

1.308210 

28 

1.072415 

1.149875 

1.232715 

1.321292 

29 

1.075096 

1.155624 

1.241959 

1.334505 

30 

1.077785 

1.161403 

1.251276 

1.347851 

31 

1.080479 

1.167210 

1.260661 

1.361329 

32 

1.083181 

1.173046 

1.270116 

1.374943 

33 

1.085889 

1.178912 

1.279642 

1.388692 

34 

1.088604 

1.184807 

1.289239 

1.402579 

35 

1.091325 

1.190731 

1.298909 

1.416605 

36 

1.094053 

1.196685 

1.308651 

1.430771 

37 

1.096788 

1.202668 

1.318466 

1.445079 

38 

1.099530 

1.208682 

1.328354 

1.459530 

39 

1.102279 

1.214725 

1.338317 

1.474125 

40 

1.105035 

1.220799 

1.348354 

1.488867 

41 

1.107798 

1.226903 

1.358467 

1.503755 

42 

1.110567 

1.233038 

1.368656 

1.518793 

43 

1.113344 

1.239203 

1.378921 

1.533981 

44 

1.116127 

1.245399 

1.389263 

1.549321 

45 

1.118918 

1.251626 

1.399682 

1.564815 

46 

1.121715 

1.257884 

1.410180 

1.580463 

47 

1.124520 

1.264174 

1.420756 

1.596267 

48 

1.127331 

1.270494 

1.431412 

1.612230 

49 

1.130149 

1.276847 

1.442148 

1.628352 

50 

1.132974 

1.283231 

1.452965 

1.644636 


3 




Rate, MX to 1% 
Year*, 51 to 75 


TABLE I 


COMPOUND INTEREST 


The value of $1 invested at a fixed rate of compound interest for one 
to one hundred years. 


Years 

%% 

%% 

%% 

1% 

51 

1.135807 

1.289647 

1.463862 

1.661083 

52 

1.138646 

1.296096 

1.474841 

1.677694 

53 

1.141493 

1.302576 

1.485902 

1.694470 

54 

1.144346 

1.309089 

1.497046 

1.711415 

55 

1.147207 

1.315634 

1.508274 

1.728530 

56 

1.150075 

1.322212 

1.519586 

1.745815 

57 

1.152950 

1.328823 

1.530983 

1.763274 

58 

1.155832 

1.335467 

1.542465 

1.780906 

59 

1.158722 

1.342145 

1.554035 

1.798715 

60 

1.161619 

1.348857 

1.565691 

1.816703 

61 

1.164523 

1.355601 

1.577434 

1.834870 

62 

1.167435 

1.362379 

1.589264 

1.853219 

63 

1.170354 

1.369191 

1.601184 

1.871751 

64 

1.173279 

1.376037 

1.613193 

1.890468 

65 

1.176212 

1.382917 

1.625293 

1.909373 

66 

1.179153 

1.389832 

1.637482 

1.928467 

67 

1.182101 

1.396781 

1.649763 

1.947752 

68 

1.185056 

1.403765 

1.662137 

1.967229 

69 

1.188019 

1.410784 

1.674603 

1.986902 

70 

1.190990 

1.417839 

1.687163 

2.006771 

71 

1.193967 

1.424928 

1.699817 

2.026839 

72 

1.196952 

1.432053 

1.712565 

2.047108 

73 

1.199945 

1.439213 

1.725409 

2.067579 

74 

1.202945 

1.446409 

1.738350 

2.088254 

75 

1.205952 

1.453641 

1.751387 

2.109137 


4 




TABLE I 


Rate, Vi% to 1% 
Year., 76 to 100 


COMPOUND INTEREST 


The value of $1 invested at a fixed rate 
to one hundred years. 

of compound interest for one 

Years 

1/4% 

%% 

%% 

1% 

76 

1.208967 

1.460909 

1.764523 

2.130229 

77 

1.211989 

1.468214 

1.777757 

2.151532 

78 

1.215019 

1.475555 

1.791090 

2.173047 

79 

1.218057 

1.482933 

1.804524 

2.194777 

80 

1.221102 

1.490349 

1.818059 

2.216726 

81 

1.224155 

1.497801 

1.831694 

2.238893 

82 

1.227215 

1.505290 

1.845433 

2.261282 

83 

1.230283 

1.512817 

1.859274 

2.283895 

84 

1.233359 

1.520381 

1.873218 

2.306734 

85 

1.236442 

1.527983 

1.887267 

2.329802 

86 

1.239533 

1.535623 

1.901422 

2.353100 

87 

1.242632 

1.543301 

1.915683 

2.376631 

88 

1.246738 

1.551018 

1.930051 

2.400397 

89 

1.248853 

1.558773 

1.944527 

2.424401 

90 

1.251976 

1.566567 

1.959111 

2.448646 

91 

1.255106 

1.574400 

1.973804 

2.473132 

92 

1.258244 

1.582272 

1.988608 

2.497864 

93 

1.261389 

1.590183 

2.003523 

2.522842 

94 

1.264543 

1.598134 

2.018549 

2.548071 

95 

1.267705 

1.606125 

2.033688 

2.573552 

96 

1.270874 

1.614156 

2.048941 

2.599287 

97 

1.274051 

1.622226 

2.064308 

2.625280 

98 

1.277237 

1.630338 

2.079791 

2.651533 

99 

1.280430 

1.638490 

2.095389 

2.678049 

100 

1.283632 

1.646683 

2.111106 

2.704830 




Rale, IVs^to 11/2% 
Years, 1 to 25 


TABLE I 


COMPOUND INTEREST 


The value of $1 invested at a fixed rate of compound interest for one 
to one hundred years. 


Years 


IVi^fo 

1%% 

1%% 

1 

1.011250 

1.012500 

1.013750 

1.015000 

2 

1.022626 

1.025156 

1.027689 

1.030225 

3 

1.034131 

1.037970 

1.041819 

1.045678 

4 

1.045764 

1.050945 

1.056144 

1.061363 

5 

1.057530 

1.064082 

1.070666 

1.077284 

6 

1.069427 

1.077383 

1.086138 

1.093442 

7 

1.083597 

1.090850 

1.100311 

1.109844 

8 

1.093624 

1.104486 

1.115411 

1.126491 

9 

1.105927 

1.118292 

1.130778 

1.143388 

10 

1.118369 

1.132270 

1.146326 

1.160539 

11 

1.130950 

1.146326 

1.162088 

1.177947 

12 

1.143674 

1.160753 

1.178066 

1.195616 

13 

1.156540 

1.175263 

1.197517 

1.213551 

14 

1.169551 

1.189953 

1.210685 

1.231754 

15 

1.182708 

1.204828 

1.227332 

1.250230 

16 

1.196013 

1.219888 

1.244207 

1.268983 

17 

1.209468 

1.235137 

1.261315 

1.288018 

13 

1.223074 

1.250576 

1.278658 

1.307338 

19 

1.236834 

1.266208 

1.296240 

1.326948 

20 

1.250749 

1.282035 

1.314062 

1.346852 

21 

1.264819 

1.298061 

1.332131 

1.367055 

22 

1.279049 

1.314286 

1.350447 

1.387560 

23 

1.293438 

1.330715 

1.369016 

1.408373 

24 

1.307989 

1.347349 

1.387839 

1.429499 

25 

1.322703 

1.364191 

1.406922 

1.450941 


6 




TABLE I 


Rate, IVeXto IViX 
Years, 26 to 50 


COMPOUND INTEREST 


The value of $1 invested at a fixed rate of compound interest for one 
to one hundred years. 


Years 

11 /8% 

1 %% 

1 %% 

1 %% 

26 

1.337584 

1.381243 

1.426267 

1.472705 

27 

1.352632 

1.398508 

1.445878 

1.494796 

28 

1.367849 

1.415989 

1.464758 

1.517218 

29 

1.383237 

1.433689 

1.485912 

1.539976 

30 

1.398798 

1.451610 

1.506343 

1.563075 

31 

1.414533 

1.469755 

1.527055 

1.586522 

32 

1.430448 

1.488127 

1.548052 

1.610320 

33 

1.446540 

1.506728 

1.569338 

1.634474 

34 

1.462813 

1.525562 

1.590916 

1.658991 

35 

1.479270 

1.544632 

1.612791 

1.683875 

36 

1.495912 

1.563940 

1.634966 

1.709133 

37 

1.512741 

1.583489 

1.657447 

1.734770 

38 

1.529759 

1.603282 

1.680237 

1.760791 

39 

1.546969 

1.623323 

1.703339 

1.787203 

40 

1.564372 

1.643615 

1.726760 

1.814011 

41 

1.581971 

1.664160 

1.750503 

1.841221 

42 

1.599768 

1.684962 

1.774572 

1.868840 

43 

1.617765 

1.706024 

1.798972 

1.896872 

44 

1.635965 

1.727349 

1.823708 

1.925325 

45 

1.654370 

1.748940 

1.848783 

1.954204 

46 

1.672981 

1.770802 

1.874204 

1.983517 

47 

1.691802 

1.792937 

1.899974 

2.013269 

48 

1.710835 

1.815348 

1.926098 

2.043468 

49 

1.730080 

1.838040 

1.952582 

2.074120 

50 

1.749544 

1.861016 

1.979429 

2.105231 




Rate, l%%to IViX 
Years, 51 to 75 


TABLE I 


COMPOUND INTEREST 


The value of $1 invested at a fixed rate of componnd interest for one 
to one hundred years. 

Years 

iVs'/o 

1V4^0 

1 %% 

1 %% 

51 

1.769227 

1.884278 

2.006646 

2.136810 

52 

1.789130 

1.907832 

2.034237 

2.168862 

53 

1.809258 

1.931679 

2.062208 

2.201395 

54 

1.829612 

1.955825 

2.090563 

2.234415 

55 

1.850195 

1.980273 

2.119308 

2.267931 

56 

1.871010 

2.005027 

2.148448 

2.301950 

57 

1.892058 

2.030089 

2.177989 

2.336479 

58 

1.913344 

2.055465 

2.207936 

2.371526 

59 

1.934869 

2.081158 

2.238294 

2.407099 

60 

1.961146 

2.107172 

2.269071 

2.443205 

61 

1.978648 

2.133512 

2.300270 

2.479853 

62 

2.000907 

2.160180 

2.331899 

2.517051 

63 

2.023417 

2.187183 

2.363962 

2.554806 

64 

2.046180 

2.214522 

2.396466 

2.593128 

65 

2.069200 

2.242204 

2.429417 

2.632024 

66 

2.092478 

2.270231 

2.462821 

2.671504 

67 

2.116018 

2.298608 

2-496686 

3.711577 

68 

2.139823 

2.327341 

2.531013 

2.752251 

69 

2.163896 

2.356433 

2.565814 

2.793534 

70 

2.188240 

2.385888 

2.601094 

2.835437 

71 

2.212858 

2.415711 

2.636858 

2.877969 

72 

2.237752 

2.445907 

2.673115 

2.921138 

73 

2.262927 

2.476481 

2.709869 

2.964955 

74 

2.288385 

2.507437 

2.747130 

3.009430 

75 

2.314129 

2.538779 

2.784902 

3.054570 


8 





TABLE I 


Rate, IVs^to IV 2 % 
Years, 76 to 100 


COMPOUND INTEREST 


The value of $1 invested at a fixed rate of compound interest for one 
to one hundred years. 


Years 


11/4% 

1 %% 

1 %% 

76 

2.340162 

2.570514 

2.823195 

3.100387 

77 

2.366489 

2.602645 

2.862003 

3.146893 

78 

2.393112 

2.635178 

2.901365 

3.194096 

79 

2.420034 

2.668118 

2.941258 

3.242006 

80 

2.447260 

2.701469 

2.981701 

3.290636 

81 

2.474791 

2.735237 

3.022698 

3.339996 

82 

2.502632 

2.769428 

3.064260 

3.390096 

83 

2.530786 

2.804045 

3.106393 

3.440947 

84 

2.559258 

2.839095 

3.149105 

3.492561 

85 

2.588049 

2.874584 

3.192405 

3.544949 

86 

2.617164 

2.910516 

3.236300 

3.598123 

87 

2.646607 

2.946897 

3.280798 

3.652095 

88 

2.676381 

2.983733 

3.325909 

3.706876 

89 

2.706491 

3.021030 

3.371640 

3.762479 

90 

2.736938 

3.058792 

3.418000 

3.818915 

91 

2.767729 

3.097027 

3.464996 

3.876198 

92 

2.798865 

3.135739 

3.512640 

3.934341 

93 

2.830349 

3.174936 

3.560937 

3.993356 

94 

2.862193 

3.214623 

3.609900 

4.053256 

95 

2.894393 

3.254805 

3.659536 

4.114053 

96 

2.926955 

3.295490 

3.709853 

4.175764 

97 

2.959883 

3.336683 

3.761729 

4.238400 

98 

2.993181 

3.378392 

3.812575 

4.301976 

99 

3.026854 

3.420622 

3.864997 

4.366505 

100 

3.060906 

3.463379 

3.918141 

4.432002 


9 





Rate, I%%to2%’ 
Years, 1 to 25 


TABLE I 


COMPOUND INTEREST 


The value of $1 invested at a fixed rate of compound interest for one 
to one hundred years. 


Years 

1 %% 

1 %% 

1 %% 

2 % 

1 

1.016250 

1.017500 

1.018750 

1.020000 

2 

1.032764 

1.035306 

1.037851 

1.040400 

3 

1.047132 

1.053424 

1.057311 

1.061208 

4 

1.066601 

1.071859 

1.077136 

1.082432 

5 

1.083933 

1.090616 

1.097332 

1.104080 

6 

1.101447 

1.109702 

1.117907 

1.126162 

7 

1.119447 

1.129122 

1.138867 

1.148684 

8 

1.137638 

1.148882 

1.160221 

1.171660 

9 

1.156124 

1.168987 

1.181975 

1.195093 

10 

1.174911 

1.189444 

1.204137 

1.218995 

11 

1.194003 

1.210260 

1.226715 

1.243375 

12 

1.213406 

1.231469 

1.249715 

1.268242 

13 

1.233123 

1.252989 

1.273148 

1.293607 

14 

1.253161 

1.274916 

1.297019 

1.319480 

15 

1.273525 

1.297227 

1.321338 

1.345869 

16 

1.294219 

1.319929 

1.346113 

1.372786 

17 

1.318282 

1.343027 

1.371353 

1.400242 

18 

1.336623 

1.366531 

1.397066 

1.428247 

19 

1.358343 

1.390444 

1.423261 

1.456812 

20 

1.380416 

1.414777 

1.449947 

1.485949 

21 

1.402847 

1.439535 

1.477133 

1.515668 

22 

1.425644 

1.464727 

1.504829 

1.545981 

23 

1.448810 

1.490360 

1.533045 

1.576901 

24 

1.472353 

1.516441 

1.561789 

1.608439 

25 

1.496279 

1.542979 

1.591073 

1.640608 


10 




TABLE I 


Rate, 1%X to 2%' 
Years, 26 to 50 


COMPOUND INTEREST 


The value of $1 invested 
to one hundred years. 

at a fixed rate 

of compound 

interest for one 

Years 

1%% 

i%% 

1%% 

2<fo 

26 

1.520593 

1.570343 

1.620905 

1.673420 

27 

1.545303 

1.597455 

1.651297 

1.706889 

28 

1.570413 

1.625411 

1.682259 

1.741027 

29 

1.595932 

1.653856 

1.713801 

1.775843 

30 

1.621866 

1.682798 

1.745935 

1.811367 

31 

1.648221 

1.712247 

1.778671 

1.847591 

32 

1.675005 

1.742211 

1.812021 

1.884543 

33 

1.702223 

1.772700 

1.845609 

1.922233 

34 

1.729844 

1.803721 

1.880609 

1.960678 

35 

1.757994 

1.835287 

1.915870 

1.999894 

36 

1.786562 

1.876404 

1.951792 

2.039892 

37 

1.815593 

1.900084 

1.988388 

2.080690 

38 

1.845096 

1.933335 

2.025670 

2.122304 

39 

1.875079 

1.967169 

2.063651 

2.164750 

40 

1.905548 

2.001594 

2.102345 

2.208045 

41 

1.936514 

2.036622 

2.141764 

2.252206 

42 

1.967981 

2.072263 

2.181922 

2.297250 

43 

1.999961 

2.108527 

2.222833 

2.343195 

44 

2.032460' 

2.145426 

2.264511 

2.390060 

45 

2.065487 

2.182971 

2.306970 

2.437861 

46 

2.099051 

2.221173 

2.350226 

2.486618 

47 

2.133160 

2.260044 

2.394292 

2.536351 

48 

2.167824 

2.299594 

2.439186 

2.587078 

49 

2.203051 

2.339837 

2.484920 

2.638820 

50 

2.238850 

2.380784 

2.531512 

2.691596 


11 




Rate, 1%X to 2% 
Years, 51 to 75 


TABLE I 


COMPOUND INTEREST 


The value of $1 invested at a fixed rate of compound interest for one 
to one hundred years. 


Years 

1%% 

1%% 

IVs^o 

2% 

51 

2.275231 

2.422447 

2.578978 

2.745428 

52 

2.312203 

2.464841 

2.627333 

2.800337 

53 

2.349776 

2.507975 

2.676596 

2.856344 

54 

2.387960 

2.551864 

2.726782 

2.913471 

55 

2.426764 

2.596522 

2.777909 

2.971741 

56 

2.466199 

2.641961 

2.829995 

3.031176 

57 

2.506273 

2.688195 

2.883057 

3.091799 

58 

2.547001 

2.735238 

2.937115 

3.153635 

59 

2.588389 

2.783105 

2.992185 

3.216708 

60 

2.630449 

2.831809 

3.048288 

3.281043 

61 

2.673194 

2.881365 

3.105444 

3.346664 

62 

2.717633 

2.931790 

3.163670 

3.413597 

63 

2.760778 

2.983096 

3.222989 

3.481869 

64 

2.805640 

3.035300 

3.283420 

3.551507 

65 

2.851231 

3.088418 

3.344984 

3.622537 

66 

2.897564 

3.142464 

3.407702 

3.694988 

67 

2.944649 

3.197457 

3.471596 

3.768888 

68 

2.992499 

3.253413 

3.536689 

3.844267 

69 

3.041126 

3.310348 

3.603001 

3.921152 

70 

3.090545 

3.368279 

3.670557 

3.999576 

71 

3.140765 

3.427224 

3.739380 

4.079568 

72 

3.191802 

3.487199 

3.809493 

4.161160 

73 

3.243669 

3.548226 

3.880921 

4.244383 

74 

3.296378 

3.610319 

3.953688 

4.329271 

75 

3.349944 

3.673500 

4.027819 

4.415856 


12 




\ 


TABLE I 


Rate, 1%X to 2% 
Years, 76 to 100 


COMPOUND INTEREST 


The value of $1 invested at a fixed rate 
to one hundred years. 

of compound 

interest for one 

Years 

1%% 

1%% 

1%% 

2<fo 

76 

3.404380 

3.737785 

4.103341 

4.504173 

77 

3.459701 

3.803196 

4.180278 

4.594257 

78 

3.515920 

3.869753 

4.258659 

4.686143 

79 

3.573053 

3.937473 

4.338508 

4.779866 

80 

3.631115 

4.006378 

4.419855 

4.875464 

81 

3.690120 

4.076491 

4.502727 

4.972973 

82 

3.750084 

4.147829 

4.587152 

5.072433 

83 

3.811023 

4.220416 

4.673161 

5.173882 

84 

3.872951 

4.294272 

4.760783 

5.277360 

85 

3.935885 

4.369422 

4.850048 

5.382907 

86 

3.999844 

4.445887 

4.940986 

5.490565 

87 

4.064840 

4.523690 

5.033629 

5.600377 

88 

4.130893 

4.602854 

5.128009 

5.712385 

89 

4.198020 

4.683403 

5.224158 

5.826633 

90 

4.266237 

4.765363 

5.322112 

5.943168 

91 

4.335563 

4.848757 

5.421901 

6.062032 

92 

4.406015 

4.933610 

5.523561 

6.183273 

93 

4.477612 

5.019948 

5.627128 

6.306938 

94 

4.550373 

5.107796 

5.732637 

6.433078 

95 

4.624316 

5.197184 

5.840123 

6.561740 

96 

4.699460 

5.288132 

5.949624 

6.692974 

97 

4.775827 

5.380675 

6.061180 

6.826834 

98 

4.853432 

5.474836 

6.174827 

6.963370 

99 

4.932300 

5.570646 

6.290604 

7.102639 

100 

5.012449 

5.668133 

6.408553 

7.244693 


13 





Rate,2y8%to2y2% 
Years, 1 to 25 


TABLE I 

COMPOUND INTEREST 


The value of $1 invested at a fixed rate of compound interest for one 
to one hundred years. 


Years 

21/8% 

2%% 

2%% 

21 / 2 % 

1 

1.021250 

1.022500 

1.023750 

1.025000 

2 

1.042951 

1.045506 

1.048064 

1.050625 

3 

1.065113 

1.069029 

1.072955 

1.076890 

4 

1.087746 

1.093082 

1.098438 

1.103813 

5 

1.110860 

1.117677 

1.124526 

1.131408 

6 

1.134465 

1.142823 

1.151233 

1.159693 

7 

1.158572 

1.168539 

1.178573 

1,188686 

8 

1.183191 

1.194830 

1.206566 

1.218403 

9 

1.208333 

1.221715 

1.235222 

1.248863 

10 

1.234013 

1.249203 

1.264559 

1.280085 

11 

1.260235 

1.277310 

1.294592 

1.312087 

12 

1.287015 

1.306049 

1.325338 

1.344890 

13 

1.314363 

1.335345 

1.356815 

1.378512 

14 

1.342293 

1.365482 

1.389030 

1.412975 

13 

1.370817 

1.396206 

1.422029 

1.448300 

16 

1.399946 

1.427620 

1.455802 

1.484507 

17 

1.429694 

1.459741 

1.490378 

1.521620 

18 

1.460075 

1.492585 

1.525774 

1.559660 

19 

1.491102 

1.526168 

1.562011 

1.598632 

20 

1.522790 

1.560508 

1.599109 

1.638619 

21 

1.555149 

1.595619 

1.637087 

1.679584 

22 

1.588195 

1.631520 

1.675958 

1.721574 

23 

1.621944 

1.668229 

1.715772 

1.764613 

24 

1.656411 

1.705764 

1.736522 

1.808729 

25 

1.691609 

1.744144 

1.798240 

1.833947 


14 





TABLE I 


Rate,2H%'to2y2% 
Years, 26 to 50 


COMPOUND INTEREST 


The value of $1 invested at a fixed rate 
to one hundred years. 

of compound 

interest for one 

Years 

21/8% 

21/4% 

2%% 

2%% 

26 

1.727555 

1.783387 

1.840948 

1.900296 

27 

1.764265 

1.823513 

1.884670 

1.947803 

28 

1.801756 

1.864542 

1.929430 

1.996498 

29 

1.840044 

1.906494 

1.975255 

2.046411 

30 

1.879144 

1.949391 

2.022167 

2.097572 

31 

1.919076 

1.993252 

2.070193 

2.150012 

32 

1.959856 

2.038100 

2.119360 

2.203762 

33 

2.001502 

2.083957 

2.169695 

2.258856 

34 

2.044034 

2.130846 

2.221225 

2.315328 

35 

2.087469 

2.178790 

2.273979 

2.373212 

36 

2.131828 

2.227812 

2.327986 

2.432543 

37 

2.177129 

2.277936 

2.383376 

2.493356 

38 

2.223393 

2.329190 

2.439878 

2.555690 

39 

2.270640 

2.381597 

2.497825 

2.619582 

40 

2.318890 

2.435186 

2.557149 

2.685072 

41 

2.368166 

2.489977 

2.617880 

2.752199 

42 

2.418490 

2.545999 

2.680055 

2.821004 

43 

2.469883 

2.603286 

2.743707 

2.891529 

44 

2.522368 

2.661859 

2.808870 

2.963818 

45 

2.575968 

2.721751 

2.875580 

3.037914 

46 

2.630707 

2.782990 

2.943875 

3.113862 

47 

2.686610 

2.845607 

3.013792 

3.191708 

48 

2.743696 

2.909633 

3.085369 

3.271501 

49 

2.801999 

2.975099 

3.158647 

3.353289 

50 

2.861541 

3.042041 

3.233665 

3.437122 


15 




Rale, 2y8%to2y2%' 
Years, 51 to 75 


table I 


COMPOUND INTEREST 


The value of $1 invested at a fixed rate of compound interest for one 
to one hundred years. 


Years 

2%% 

. 2y4% 

2%% 

2V2<fo 

51 

2.922348 

3.110487 

3.310464 

3.523050 

52 

2.984447 

3.180473 

3.389088 

3.611127 

53 

3.047866 

3.252033 

3.469578 

3.701405 

54 

3.112633 

3.325203 

3.551981 

3.793941 

55 

3.178777 

3.400020 

3.636340 

3.888790 

56 

3.246326 

3.476520 

3.722703 

3.986010 

57 

3.315312 

3.554742 

3.811118 

4.085661 

58 

3.385763 

3.634724 

3.901631 

4.187803 

59 

3.457710 

3.716505 

3.994295 

4.292498 

60 

3.531182 

3.800126 

4.089158 

4.399811 

61 

3.606219 

3.885629 

4.186277 

4.509806 

62 

3.682851 

3.973055 

4.285700 

4.622552 

63 

3.761111 

4.062449 

4.387486 

4.738116 

64 

3.841034 

4.153854 

4.491688 

4.856569 

65 

3.922654 

4.247316 

4.598366 

4.977983 

66 

4.006010 

4.342881 

4.707576 

5.102433 

67 

4.091137 

4.440595 

4.819381 

5.229994 

68 

4.178073 

4.540508 

4.933842 

5.360744 

69 

4.266857 

4.642669 

5.051020 

5.494764 

70 

4.357526 

4.747129 

5.170982 

5.632134 

71 

4.450123 

4.853939 

5.293792 

5.772938 

72 

4.544688 

4.963152 

5.419520 

5.917262 

73 

4.641261 

5.074823 

5.548234 

6.065194 

74 

4.739887 

5.189006 

5.680004 

6.216824 

75 

4.840609 

5.305759 

5.814903 

6.372245 


16 




TABLE I 


Rate,2y8>^lo2V2% 
Years, 76 to 100 


COMPOUND INTEREST 


The value of $1 invested at a fixed rate 
to one hundred years. 

of compound 

interest for one 

Years 

2Vs<fo 

2%% 

2%% 

2y2% 

76 

4.943471 

5.425139 

5.953007 

6.531552 

77 

5.048519 

5.547204 

6.094390 

6.694841 

78 

5.155800 

5.672016 

6.239033 

6.862212 

79 

5.265360 

5.799636 

6.387311 

7.033768 

80 

5.377247 

5.930127 

6.539010 

7.209613 

81 

5.491513 

6.063555 

6.694310 

7.389854 

82 

5.608207 

6.199985 

6.853302 

7.574601 

83 

5.727381 

6.339484 

7.016066 

7.763967 

84 

5.849087 

6.482122 

7.182699 

7.958066 

85 

5.973379 

6.627970 

7.353287 

8.157019 

86 

6.100313 

6.777099 

7.527927 

8.360946 

87 

6.229944 

6.929584 

7.706714 

8.569971 

88 

6.362331 

7.083499 

7.889749 

8.784221 

89 

6.497530 

7.244923 

8.077130 

9.003828 

90 

6.635596 

7.407932 

8.268962 

9.228924 

91 

6.776602 

7.574611 

8.465349 

9.459647 

92 

6.920604 

7.745039 

8.666402 

9.696139 

93 

7.067666 

7.919302 

8.872228 

9.938542 

94 

7.217854 

8.097487 

9.082944 

10.18701 

95 

7.371230 

8.279679 

9.298662 

10.44168 

96 

7.527868 

8.465972 

9.519506 

10.70272 

97 

7.687835 

8.656456 

9.745592 

10.97029 

98 

7.851202 

8.851226 

9.977050 

11.24455 

99 

8.018037 

9.050378 

10.21400 

11.52567 

100 

8.188419 

9.254010 

10.43659 

11.81381 


7 


17 




Rate, 2%% to Z% 
Years, 1 to 25 


TABLE I 


COMPOUND INTEREST 


. The value of $1 invested at a fixed rate of compound interest for one 
to one hundred years. 


Years 

2%fo 

2%% 

2%fo 

3% 

1 

1.026250 

1.027500 

1.028750 

1.030000 

2 

1.053189 

1.055756 

1.058326 

1.060900 

3 

1.080835 

1.084789 

1.088753 

1.092727 

4 

1.109206 

1.114621 

1.120055 

1.125509 

3 

1.138323 

1.145273 

1.152256 

1.159274 

6 

1.168204 

1.176768 

1.185383 

1.194051 

7 

1.198869 

1.209129 

1.219463 

1.229873 

8 

1.230339 

1.242380 

1.254522 

1.266769 

9 

1.262635 

1.276545 

1.290590 

1.304772 

10 

1.295779 

1.311650 

1.327694 

1.343915 

11 

1.329793 

1.347720 

1.365865 

1.384233 

12 

1.364700 

1.384783 

1.405033 

1.425760 

13 

1.400523 

1.422864 

1.445531 

1.468532 

14 

1.437287 

1.461993 

1.487090 

1.512588 

15 

1.475015 

1.502198 

1.527731 

1.557966 

16 

1.513734 

1.543508 

1.573826 

1.604705 

17 

1.553469 

1.585955 

1.602384 

1.652846 

18 

1.594248 

1.629568 

1.665622 

1.702431 

19 

1.636096 

1.674381 

1.713508 

1.753504 

20 

1.679043 

1.720426 

1.762772 

1.806109 

21 

1.723118 

1.767738 

1.813450 

1.860292 

22 

1.768350 

1.816351 

1.865587 

1.916101 

23 

1.814768 

1.866300 

1.919223 

1.973584 

24 

1.862406 

1.917623 

1.974400 

2.032791 

25 

1.911294 

1.970357 

2.031164 

2.093774 


18 




TABLE I 

COMPOUND INTEREST 


Rale, 2%% to 3% 
Years, 26 to 50 


The value of $1 invested at a fixed rate of compound interest for one 
to one hundred years. 


Years 

2%% 

2%% 

2%% 

3^0 

26 

1.961465 

2.024542 

2.089560 

2.156587 

27 

2.012953 

2.080216 

2.149634 

2.221285 

28 

2.065793 

2.137422 

2.211279 

2.287924 

29 

2.120020 

2.196201 

2.274562 

2.356561 

30 

2.175670 

2.256597 

2.340421 

2.427257 

31 

2.232781 

2.318653 

2.407708 

2.500075 

32 

2.291391 

2.382416 

2.476929 

2.575077 

33 

2.351540 

2.447932 

2.548141 

2.652329 

34 

2.413267 

2.515250 

2.621400 

2.731899 

35 

2.476615 

2.584419 

2.696764 

2.813856 

36 

2.541526 

2.65549f 

2.774296 

2.898272 

37 

2.608343 

2.728517 

2.854057 

2.985220 

38 

2.676812 

2.803551 

2.936110 

3.074777 

39 

2.747077 

2.880648 

3.020523 

3.167020 

40 

2.819188 

2.959865 

3.107363 

3.262030 

41 

2.893191 

3.041261 

3.196700 

3.359891 

42 

2.969137 

3.124896 

3.288604 

3.460687 

43 

3.047146 

3.210830 

3.383151 

3.564508 

44 

3.127061 

3.299128 

3.480416 

3.671443 

45 

3.209146 

3.389854 

3.580478 

3.781586 

46 

3.293385 

3.483075 

3.683416 

3.895034 

47 

3.379836 

3.578859 

3.789314 

4.011885 

48 

3.468556 

3.677278 

3.898256 

4.132241 

49 

3.559606 

3.778403 

4.010331 

4.256208 

50 

3.653044 

3.882308 

4.125628 

4.383894 


19 





Rate, 2%% to 3% 
Years, 51 to 75 


TABLE I 


COMPOUND INTEREST 


The value of $1 invested at a fixed rate of compound interest for one 
to one hundred years. 

Years 

2%% 

2%% 

2%% 

3% 

51 

3.748936 

3.989071 

4.244239 

4.515411 

52 

3.847345 

4.098771 

4.366260 

4.650873 

53 

3.948338 

4.211487 

4.491790 

4.790399 

54 

4.051981 

4.327302 

4.620928 

4.934110 

55 

4.158345 

4.446302 

4.753769 

5.082133 

56 

4.267501 

4.568575 

4.890449 

5.234597 

57 

4.379520 

4.694211 

5.031050 

5.391634 

58 

4.494483 

4.823301 

5.175691 

5.553383 

59 

4.612463 

4.955942 

5.324492 

5.719985 

60 

4.733539 

5.092229 

5.477571 

5.891582 

61 

4.857794 

5.232265 

5.635050 

6.068329 

62 

4.985310 

5.376152 

5.797057 

6.250397 

63 

5.116173 

5.523996 

5.963721 

6.437890 

64 

5.250472 

5.675906 

6.135158 

6.631027 

65 

5.388296 

5.831993 

6.311564 

6.829957 

66 

5.529739 

5.992373 

6.493021 

7.034855 

67 

5.674894 

6.157163 

6.679693 

7.245901 

68 

5.823858 

6.326484 

6.871735 

7.463278 

69 

5.976733 

6.500462 

7.069296 

7.687175 

70 

6.133621 

6.679225 

7.272538 

7.917790 

71 

6.294629 

6.862904 

7.481621 

8.155324 

72 

6.459861 

7.051632 

7.696717 

8.399983 

73 

6.629431 

7.245551 

7.917997 

8.651983 

74 

6.803453 

7.444803 

8.145640 

8.911542 

75 

6.982043 

7.649533 

8.379826 

9.178888 


20 




TABLE I 

COMPOUND INTEREST 


Rate, 2%% to 3% 
Years, 76 to 1 


The value of $1 invested at a fixed rate of compound interest for one 
to one hundred years. 


Years 

2%% 

2%% 

278% 

3% 

76 

7.165320 

7.859895 

8.620746 

9.454255 

77 

7.353409 

8.076042 

8.868590 

9.737882 

78 

7.546435 

8.298133 

9.123562 

10.03002 

79 

7.744527 

8.526331 

9.385862 

10.33092 

80 

7.947820 

8.760804 

9.655704 

10.64084 

81 

8.156449 

9.001726 

9.933305 

10.96007 

82 

8.370554 

9.249273 

10.21889 

11.28887 

83 

8.590280 

9.503628 

10.51268 

11.62754 

84 

8.815774 

9.764978 

10.81492 

11.97636 

85 

9.047186 

10.03351 

11.12584 

12.33565 

86 

9.284672 

10.30943 

11.44571 

12.70572 

87 

9.528494 

10.59294 

11.77477 

13.08689 

88 

9.780764 

10.88425 

12.14122 

13.47950 

89 

10.03520 

11.18356 

12.46155 

13.88388 

90 

10.29862 

11.49111 

12.90590 

14.30039 

91 

10.56895 

11.80711 

13.18839 

14.72940 

92 

10.84888 

12.13181 

13.56576 

15.17128 

93 

11.13110 

12.46543 

13.95762 

15.62642 

94 

11.42330 

12.80822 

14.35890 

16.09521 

95 

11.72315 

13.16046 

14.77172 

16.57807 

96 

12.03088 

13.52237 

15.19640 

17.07541 

97 

12.34669 

13.89424 

15.63330 

17.18767 

98 

12.67079 

14.27633 

16.08275 

18.11530 

99 

13.00340 

14.66893 

16.54513 

18.65876 

100 

13.34474 

15.07232 

17.02080 

19.21852 


21 




Rate,3y8>^to3y2%- 
Years, 1 to 25 


TABLE I 


COMPOUND INTEREST 


The value of $1 invested at a fixed rate of compound interest for one 
to one hundred years. 


Years 

3%% 

3y4% 

3%% 

3%% 

1 

1.031250 

1.032500 

1.033750 

1.035000 

2 

1.063476 

1.066056 

1.068639 

1.071225 

3 

1.096710 

1.100703 

1.104705 

1.108717 

4 

1.130982 

1.136476 

1.141990 

1.147522 

5 

1.166325 

1.173412 

1.180531 

1.187685 

6 

1.202772 

1.211548 

1.220374 

1.229254 

7 

1.240359 

1.250923 

1.264470 

1.272278 

8 

1.279120 

1.291578 

1.304139 

1.316807 

9 

1.319092 

1.333554 

1.348154 

1.362896 

10 

1.360313 

1.376895 

1.393654 

1.410597 

11 

1.402823 

1.421644 

1.440690 

1.459967 

12 

1.446661 

1.467848 

1.489313 

1.511066 

13 

1.491869 

1.515553 

1.539577 

1.563953 

14 

1.538490 

1.564809 

1.591538 

1.618691 

15 

1.586567 

1.615666 

1.645252 

1.675345 

16 

1.636147 

1.668175 

1.700780 

1.733982 

17 

1.687276 

1.722391 

1.758180 

1.794672 

18 

1.740004 

1.778368 

1.817519 

1.857485 

19 

1.794379 

1.836165 

1.878860 

1.922498 

20 

1.850453 

1.895841 

1.942272 

1.989784 

21 

1.908279 

1.957456 

2.007824 

2.059426 

22 

1.967913 

2.021073 

2.075587 

2.131506 

23 

2.029410 

2.086758 

2.145638 

2.206109 

24 

2.092828 

2.154578 

2.218054 

2.283322 

25 

2.158229 

2.224603 

2.292913 

2.363238 





TABLE I 


Rate.3y8%'lo3y2% 
Years, 26 to 50 


COMPOUND INTEREST 


The value of $1 invested at a fixed rate of compound interest for one 
to one hundred years. 


Years 

3%% 

3%% 

3%fo 


26 

2.225673 

2.296903 

2.370298 

2.445952 

27 

2.295225 

2.371552 

2.450296 

2.531560 

28 

2.366951 

2.448628 

2.532993 

2.620163 

29 

2.440917 

2.528208 

2.618481 

2.711868 

30 

2.517196 

2.610375 

2.706855 

2.806784 

31 

2.595858 

2.695212 

2.798210 

2.905022 

32 

2.676978 

2.782807 

2.892651 

3.006697 

33 

2.760633 

2.873248 

2.990278 

3.111930 

34 

2.846903 

2.966629 

3.091199 

3.220848 

35 

2.935867 

3.063046 

3.195527 

3.333577 

36 

3.027613 

3.162595 

3.303376 

3.450252 

37 

3.122226 

3.265380 

3.414865 

3.571010 

38 

3.219794 

3.371505 

3.530117 

3.695996 

39 

3.320413 

3.481079 

3.649257 

3.825355 

40 

3.424176 

3.594215 

3.772420 

3.959242 

41 

3.531181 

3.711027 

3.899739 

4.097815 

42 

3.641529 

3.831636 

4.031355 

4.241238 

43 

3.755327 

3.956164 

4.167413 

4.389682 

44 

3.872680 

4.084740 

4.308063 

4.543320 

45 

3.993701 

4.217494 

4.453459 

4.702334 

46 

4.118503 

4.354561 

4.603764 

4.866915 

47 

4.247206 

4.496085 

4.759140 

5.037257 

48 

4.379930 

4.642208 

4.919761 

5.213561 

49 

4.516802 

4.792080 

5.085802 

5.396034 

50 

4.657951 

4.948858 

5.257448 

5.584895 


23 




Rate, 3y8%to 3Vi% 
Years, 51 to 75 


TABLE I 


COMPOUND INTEREST 


The value of $1 invested at a fixed rate of compound interest for one 
to one hundred years. 


Years 

31 / 8 % 

3%fo 

3%fo 

31/2^0 

51 

4.803512 

5.109696 

5.434886 

5.780366 

52 

4.953621 

5.275761 

5.618314 

5-982678 

53 

5.108421 

5.447224 

5.807931 

6.192071 

54 

5.268058 

5.624259 

6.003948 

6.408793 

55 

5.432685 

5.807049 

6.206581 

6.633100 

56 

5.602455 

5.995778 

6.416053 

6.865256 

57 

5.777530 

6.190641 

6.632595 

7.105541 

58 

5.958078 

6.391837 

6.856445 

7.354233 

59 

6.144267 

6.589572 

7.087849 

7.611630 

60 

6.336274 

6.814062 

7.327065 

7.878035 

61 

6.534281 

7.035519 

7.574352 

8.153766 

62 

6.738478 

7.264174 

7.829985 

8.439148 

63 

6.949053 

7.500260 

8.094247 

8.734518 

64 

7.166212 

7.744019 

8.367429 

9.040224 

65 

7.390153 

7.995700 

8.649828 

9.356630 

66 

7.621095 

8.255560 

8.941760 

9.684112 

67 

7.859254 

8.523866 

9.243544 

10.02306 

68 

8.104854 

8.800892 

9.555512 

10.37387 

69 

8.358129 

9.086921 

9.878012 

10.73694 

70 

8.619320 

9.382250 

10.21139 

11.11273 

71 

8.888672 

9.687173 

10.55603 

11.50168 

72 

9.166442 

10.00201 

10.91229 

11.90424 

73 

9.452892 

10.32707 

11.28058 

12.32088 

74 

9.748292 

10.66270 

11.66120 

12.75211 

75 

10.05293 

11.00924 

12.05487 

13.19843 


24 





TABLE I 


Rate, aVsXtoSVsX 
Years, 76 to 100 


COMPOUND INTEREST 


The value of $1 invested at a fixed rate of compound interest; for one 
to one hundred years. 


Years 

31 / 8 % 

31 / 4 % 

3%% 


76 

10.36708 

11.36704 

12.46172 

13.66038 

77 

10.69105 

11.73647 

12.88230 

14.13849 

78 

11.02514 

12.11791 

13.31708 

14.63334 

79 

11.36967 

12.51174 

13.76653 

15.14550 

80 

11.72497 

12.91838 

14.23115 

15.67559 

81 

12.09138 

13.33823 

14.71145 

16.22423 

82 

12.46923 

13.77172 

15.20796 

16.79208 

83 

12.85890 

14.21930 

15.72123 

17.37980 

84 

13.26073 

14.68143 

16.25182 

17.98809 

85 

13.67513 

15.15858 

16.80032 

18.61767 

86 

14.10248 

15.65124 

17.36733 

19.26929 

87 

14.54318 

16.15991 

17.95347 

19.94372 

88 

14.99765 

16.68511 

18.55940 

20.64175 

89 

15.46632 

17.22738 

19.17695 

21.36421 

90 

15.94964 

17.78726 

19.83330 

22.11195 

91 

16.44807 

18.36535 

20.50267 

22.88587 

92 

16.96207 

18.96222 

21.19464 

23.18687 

93 

17.49213 

19.57850 

21.90996 

24.51591 

94 

18.03875 

20.21480 

22.64942 

25.37396 

95 

18.60246 

20.87178 

23.41383 

26.26204 

96 

19.18379 

21.55012 

24.20405 

27.18121 

97 

19.78348 

22.25050 

25.02093 

28.13255 

98 

20.40150 

22.97364 

25.86539 

29.11719 

99 

21.03905 

23.72028 

26.73834 

30.13629 

100 

21.69651 

24.49119 

27.64077 

31.19105 


25 




Rate, 3%% to 4% 
Year*, 1 to 2S 


TABLE I 


COMPOUND INTEREST 


The value of $1 invested at a fixed rate 
to one hundred years. 

of compound 

interest for one 

Years 

3%% 

3%% 

3%% 

4% 

1 

1.036250 

1.037500 

1.038750 

1.040000 

2 

1.073814 

1.076406 

1.079001 

1.081600 

3 

1.112740 

1.116772 

1.120813 

1.124864 

4 

1.153076 

1.158651 

1.164244 

1.169858 

5 

1.194875 

1.202100 

1.209358 

1.216652 

6 

1.238189 

1.247179 

1.256221 

1.265318 

7 

1.283073 

1.293948 

1.304900 

1.315930 

8 

1.329584 

1.342471 

1.355464 

1.368568 

9 

1.377782 

1.392814 

1.407988 

1.423310 

10 

1.427726 

1.445044 

1.462547 

1.480243 

11 

1.479481 

1.499233 

1.519221 

1.539452 

12 

1.533112 

1.555455 

1.578091 

1.601030 

13 

1.588687 

1.613785 

1.639242 

1.665071 

14 

1.646277 

1.674302 

1.702762 

1.731674 

15 

1.705955 

1.737087 

1.768744 

1.800941 

16 

1.767795 

1.802228 

1.837283 

1.872978 

17 

1.831879 

1.869812 

1.908477 

1.947897 

18 

1.898283 

1.939930 

1.982430 

2.025813 

19 

1.967096 

2.016677 

2.059250 

2.106846 

20 

2.038403 

2.088151 

2.139045 

2.191119 

21 

2.112290 

2.166457 

2.221933 

2.278764 

22 

2.188865 

2.247699 

2.308033 

2.369914 

23 

2.268212 

2.331988 

2.397469 

2.464711 

24 

2.350433 

2.419437 

2.490371 

2.563299 

25 

2.435637 

2.510166 

2.586873 

2.665830 


26 





TABLE I 


Rate, 3%X to 4%' 
Years, 26 to 50 


COMPOUND INTEREST 

The value of $1 invested at a fixed rate of compound interest for one 
to one hundred years. 


Years 

3%% 

3%^o 

3y8% 

4% 

26 

2.523928 

2.604297 

2.687114 

2.772463 

27 

2.615420 

2.701958 

2.791238 

2.883362 

28 

2.710229 

2.803282 

2.899400 

2.998696 

29 

2.808475 

2.908405 

3.011751 

3.118644 

30 

2.910281 

3.017470 

3.128455 

3.243388 

31 

3.015780 

3.130625 

3.249683 

3.373124 

32 

3.125101 

3.248024 

3.375608 

3.508048 

33 

3.238385 

3.369825 

3.506412 

3.648370 

34 

3.355776 

3.496193 

3.642286 

3.794304 

35 

3.477423 

3.627300 

3.783424 

3.946076 

36 

3.603480 

3.763324 

3.930031 

4.103919 

37 

3.734105 

3.904449 

4.082320 

4.268075 

38 

3.869465 

4.050865 

4.240509 

4.438799 

39 

4.009734 

4.202773 

4.404828 

4.616350 

40 

4.155086 

4.360377 

4.575514 

4.801003 

41 

4.305707 

4.523891 

4.752816 

4.993043 

42 

4.461790 

4.693537 

4.936988 

5.192765 

43 

4.623527 

4.869545 

5.128295 

5.400475 

44 

4.791131 

5.052152 

5.253926 

5.616493 

45 

4.964808 

5.241607 

5.533438 

5.841151 

46 

5.144782 

5.438167 

5.747858 

6.074797 

47 

5.331280 

5.642099 

5.970587 

6.317788 

48 

5.524541 

5.853677 

6.201946 

6.570499 

49 

5.724808 

6.073190 

6.442271 

6.833319 

50 

5.932325 

6.300934 

6.691909 

7.106650 


27 




R«te, to A% 
Years* 51 to 76 


TABLE I 


COMPOUND INTEREST 


The value of $1 invested at a fixed rate of compound interest for one 
to one hundred years. 


Years 

3%% 

3%% 

3%% 

4% 

51 

6.147371 

6.537219 

6.951220 

7.390916 

52 

6.370213 

6.782365 

7.220578 

7.686553 

53 

6.601133 

7.036703 

7.500375 

7.994015 

54 

6.840423 

7.300580 

7.791014 

8.313775 

55 

7.088388 

7.574352 

8.092916 

8.646326 

56 

7.345342 

7.858390 

8.406516 

8.992178 

57 

7.611609 

8.153079 

8.732268 

9.351865 

58 

7.887520 

8.458820 

9.070642 

9.725940 

59 

8.173450 

8.776025 

9.422129 

10.11497 

60 

8.469738 

9.105126 

9.787234 

10.51957 

61 

8.776766 

9.446568 

10.16649 

10.94035 

62 

9.094922 

9.800815 

10.56044 

11.37796 

63 

9.424612 

10.16835 

10.96966 

11.83308 

64 

9.766252 

10.54966 

11.39473 

12.30640 

65 

10.12028 

10.94527 

11.83627 

12.79866 

66 

10.48714 

11.35572 

12.29493 

13.31060 

67 

10.86730 

11.78156 

12.77135 

13.84302 

68 

11.26123 

12.22336 

13.26625 

14.39674 

69 

11.66945 

12.68174 

13.78031 

14.97261 

70 

12.09247 

13.15731 

14.31430 

15.57151 

71 

12.53082 

13.65071 

14.86896 

16.19437 

72 

12.98506 

14.16261 

15.44515 

16.84214 

73 

13.45577 

14.69371 

16.04364 

17.51583 

74 

13.94354 

15.24472 

16.66533 

18.21646 

75 

14.44899 

15.81639 

17.31111 

18.94512 


28 





TABLE I 


Rate, 3%^ to 4% 
Years, 76 to 100 


COMPOUND INTEREST 


The value of $1 invested at a fixed rate of compound interest for one 
to one hundred years. 


Years 

3%% 

3%% 

3%% 

4% 

76 

14.97287 

16.40951 

17.98192 

19.70292 

77 

15.51552 

17.02486 

18.67872 

20.49104 

78 

16.07797 

17.66329 

19.40251 

21.31068 

79 

16.66078 

18.32567 

20.15436 

22.16311 

80 

17.26474 

19.01289 

20.93534 

23.04963 

81 

17.89058 

19.72587 

21.74658 

23.97162 

82 

18.53912 

20.46559 

22.58926 

24.93048 

83 

19.21115 

21.23301 

23.46459 

25.92770 

84 

19.90756 

22.02929 

24.37384 

26.96480 

85 

20.62920 

22.85538 

25.31833 

28.04339 

86 

21.37701 

23.71246 

26.26915 

29.16512 

87 

22.15193 

24.60167 

27.31851 

30.33172 

88 

22.95493 

25.52423 

28.37710 

31.54500 

89 

23.78704 

26.48139 

29.47671 

32.80679 

90 

24.64932 

27.47445 

30.61893 

34.11905 

91 

25.54286 

28.50474 

31.80541 

35.48381 

92 

26.46879 

29.57367 

33.03787 

36.90315 

93 

27.42828 

30.68268 

34.31808 

38.37928 

94 

28.42255 

31.83328 

35.64462 

39.91445 

95 

29.45286 

33.02703 

37.02926 

41.51102 

96 

30.52052 

34.26554 

38.46414 

43.17146 

97 

31.62690 

35.55050 

39.95462 

44.89831 

98 

32.77336 

36.88364 

41.50286 

46.69424 

99 

33.96139 

38.26678 

43.11109 

48.56201 

100 

35.19250 

39.70178 

44.78164 

50.50449 


29 




Rat., 4ys%lo4>/2% 
Years, 1 to 25 


TABLE I 


COMPOUND INTEREST 


The value of $1 invested at a fixed rate of compound interest for one 
to one hundred years. 


Years 

4%% 

4%% 

4%% 

4%% 

1 

1.041250 

1.042500 

1.043750 

1.045000 

2 

1.084201 

1.086806 

1.089414 

1.092025 

3 

1.128925 

1.132955 

1.137076 

1.141166 

4 

1.175493 

1.181148 

1.186823 

1.192518 

5 

1.223954 

1.231347 

1.238747 

1.246181 

6 

1.274471 

1.283679 

1.292942 

1.302260 

7 

1.327043 

1.338236 

1.349508 

1.360862 

8 

1.381783 

1.395111 

1.408549 

1.422101 

9 

1.438782 

1.454403 

1.470173 

1.486095 

10 

1.498132 

1.516216 

1.534493 

1.552965 

11 

1.559930 

1.580655 

1.601627 

1.622853 

12 

1.624277 

1.647833 

1.671699 

1.695881 

13 

1.691278 

1.717866 

1.744835 

1.772196 

14 

1.761043 

1.790875 

1.821171 

1.851945 

15 

1.833686 

1.866988 

1.900848 

1.935283 

16 

1.909326 

1.946335 

1.984010 

2.022370 

17 

1.983516 

2.029054 

2.070811 

2.113377 

18 

2.070094 

2.115289 

2.161409 

2.208479 

19 

2.155485 

2.205189 

2.255971 

2.307860 

20 

2.244398 

2.298910 

2.354670 

2.411715 

21 

2.336980 

2.396614 

2.457686 

2.520242 

22 

2.433381 

2.498470 

2.565210 

2.633653 

23 

2.533746 

2.604655 

2.677438 

2.752167 

24 

2.638274 

2.715353 

2.794576 

2.876015 

25 

2.747103 

2.830757 

2.916839 

3.005436 


30 





TABLE I 


Rate, 4%^^ to 4%%' 
Yearsp 26 to 50 


COMPOUND INTEREST 


The value of $1 invested at a fixed rate of compound interest for one 
to one hundred years. 


Years 

4%% 

41 / 4 % 

4%% 


26 

2.860421 

2.951064 

3.044451 

3.140681 

27 

2.977728 

3.076484 

3.177646 

3.282011 

28 

3.101273 

3.207235 

3.316668 

3.429702 

29 

3.214364 

3.343543 

3.461772 

3.584038 

30 

3.362405 

3.485644 

3.613225 

3.745319 

31 

3.501104 

3.633784 

3.771303 

2.913859 

32 

3.645524 

3.788220 

3.936298 

4.089982 

33 

3.795902 

3.949219 

4.108511 

4.274032 

34 

3.952483 

4.117061 

4.288259 

4.466364 

35 

4.115523 

4.292038 

4.475870 

4.667351 

36 

4.285288 

4.474449 

4.671690 

4.877382 

37 

4.462055 

4.664613 

4.876077 

5.096864 

38 

4.646115 

4.862859 

5.089405 

5.326223 

39 

4.837768 

5.069531 

5.312066 

5.565903 

40 

5.037326 

5.284987 

5.544469 

5.816369 

41 

5.245115 

5.509599 

5.787040 

6.078106 

42 

5.461476 

5.743757 

6.040224 

6.351620 

43 

5.686761 

5.987867 

6.304484 

6.637443 

44 

5.921340 

6.242352 

6.580305 

6.936128 

45 

6.165596 

6.507654 

6.868193 

7.248253 

46 

6.419926 

6.784230 

7.168676 

7.574425 

47 

6.684748 

7.072560 

7.482307 

7.915275 

48 

6.960493 

7.373144 

7.809657 

8.271463 

49 

7.247613 

7.686504 

8.151330 

8.643679 

50 

7.546577 

8.013182 

8.507950 

9.032646 


31 




RaU,4»A%to 4hi% 
Year«» 51 to 75 


TABLE I 


COMPOUND INTEREST 

The value of $1 invested at a fixed rate of compound interest for one 
to one hundred years. 


Years 


4%% 

4%% 

4^4% 

51 

7.857872 

8.353743 

8.880174 

9.439115 

52 

8.182010 

8.708777 

9.268682 

9.863876 

53 

8.519518 

9.078900 

9.674187 

10.30775 

54 

8.870946 

9.464755 

10.09743 

10.77160 

55 

9.236874 

9.867010 

10.53920 

11.25632 

56 

9.617894 

10.28636 

11.00029 

11.76285 

57 

10.01463 

10.72353 

11.48155 

12.29218 

58 

10.42774 

11.17928 

11.98386 

12.84533 

59 

10.85788 

11.65440 

12.50816 

13.42337 

60 

11.30577 

12.14971 

13.05539 

14.02742 

61 

11.79926 

12.66607 

13.62657 

14.65866 

62 

12.25773 

13.20438 

14.22273 

15.31830 

63 

12.76336 

13.76557 

14.84497 

16.00762 

64 

13.28985 

14.35061 

15.49444 

16.72796 

65 

13.83805 

14.96051 

16.17233 

17.48072 

66 

14.40887 

15.59633 

16.87987 

18.26735 

67 

15.00324 

16.25918 

17.61836 

19.08938 

68 

15.62212 

16.95020 

18.38916 

19.94841 

69 

16.26653 

17.67058 

19.19369 

20.84609 

70 

16.93753 

18.42159 

20.03341 

21.78417 

71 

17.63620 

19.20451 

20.90988 

22.76446 

72 

18.36369 

20.02070 

21.82469 

23.78886 

73 

19.12120 

20.87158 

22.77952 

24.85936 

74 

19.90994 

21.75862 

23.77612 

25.97803 

75 

20.73122 

22.68337 

24.81632 

27.14704 


32 





TABLE I 


Rate,4y8%to4y2% 
Years, 76 to lOQ 


COMPOUND INTEREST 


The value of $1 invested at a fixed rate of compound interest for one 
to one hundred years. 


Years 

41 / 8 % 

41 / 4 % 

4%% 


76 

21.58639 

23.64741 

25.90204 

28.36866 

77 

22.47683 

24.65243 

27.03526 

29.64525 

78 

23.40400 

25.70016 

28.21805 

30.97929 

79 

24.36941 

26.79241 

29.45260 

32.37335 

80 

25.37465 

27.93109 

30.74114 

33.83015 

81 

26.42104 

29.11816 

32.08607 

35.35251 

82 

27.51123 

30.35568 

33.48984 

36.94337 

83 

28.64607 

31.64580 

34.95502 

38.60583 

84 

29.82771 

32.99075 

36.48430 

40.34309 

85 

31.05811 

34.39287 

38.08049 

42.15853 

86 

32.33925 

35.85457 

39.74651 

44.05567 

87 

33.67325 

37.37839 

41.48542 

46.03817 

88 

35.06226 

38.96697 

43.30041 

48.10989 

89 

36.50858 

40.62307 

45.19480 

50.27484 

90 

38.01456 

42.34957 

47.17208 

52.53721 

91 

39.58266 

44.14941 

49.23586 

54.90139 

92 

41.21545 

46.02576 

51.38992 

57.37195 

93 

42.91558 

47.98186 

53.63824 

59.95369 

94 

44.68584 

50.02110 

55.98491 

62.65161 

95 

46.52914 

52.14702 

58.43425 

65.47093 

96 

48.44846 

54.36327 

60.99079 

68.41712 

97 

50.44697 

56.67371 

63.65910 

71.49589 

98 

52.52789 

59.08235 

66.44418 

74.71321 

99 

54.69468 

61.59336 

69.35113 

78.07531 

100 

56.95081 

64.21109 

72.38523 

81.58870 


8 33 




Rate, 4%% to 5% 
Years, 1 to 25 


TABLE I 

COMPOUND INTEREST 


The value of $1 invested at a fixed rate of compound interest for one 
to one hundred years. 


Years 

4%% 


4%% 

5% 

1 

1.046250 

1.047500 

1.048750 

1.050000 

2 

1.094639 

1.097256 

1.099876 

1.102500 

3 

1.145266 

1.149376 

1.153496 

1.157625 

4 

1.198234 

1.203971 

1.209729 

1.215506 

5 

1.253652 

1.261116 

1.268703 

1.276281 

6 

1.311633 

1.321065 

1.330552 

1.340095 

7 

1.372296 

1.383815 

1.395417 

1.407100 

8 

1.435765 

1.449546 

1.463444 

1.477455 

9 

1.502168 

1.518400 

1.534787 

1.551328 

10 

1.571643 

1.590523 

1.609607 

1.628894 

11 

1.644331 

1.666073 

1.688076 

1.710339 

12 

1.720381 

1.745211 

1.770370 

1.795856 

13 

1.799949 

1.828109 

1.856676 

1.885649 

14 

1.883196 

1.914944 

1.947188 

1.979931 

15 

1.970294 

2.005903 

2.042114 

2.078928 

16 

2.061420 

2.101183 

2.141667 

2.182874 

17 

2.161732 

2.200990 

2.246074 

2.292018 

18 

2.256510 

2.305536 

2.355570 

2.406619 

19 

2.360873 

2.415050 

2.470404 

2.526950 

20 

2.470063 

2.529764 

2.590836 

2.653297 

21 

2.584303 

2.649927 

2.717140 

2.785962 

22 

2.703826 

2.775799 

2.849601 

2.925260 

23 

2.828878 

2.907649 

2.988518 

3.071523 

24 

2.959713 

3.045762 

3.134209 

3.225099 

25 

3.096599 

3.190436 

3.287002 

3.386354 


34 





TABLE I 


R.te. 4%% to 5% 
Years, 26 to 50 


COMPOUND INTEREST 

The value of $1 invested at a fixed rate of compound interest for one 
to one hundred years. 


Years 

4%% 

4%% 

4%% 

5% 

26 

3.239817 

3.341982 

3.447244 

3.555672 

27 

3.389657 

3.500725 

3.615298 

3.733456 

28 

3.546428 

3.667009 

3.791543 

3.920129 

29 

3.710450 

3.841192 

3.976381 

4.116135 

30 

3.882068 

4.023648 

4.170230 

4.321943 

31 

4.061602 

4.214771 

4.373529 

4.538040 

32 

4.249451 

4.414972 

4.586738 

4.764942 

33 

4.445987 

4.624683 

4.810342 

5.003189 

34 

4.651613 

4.844355 

5.044847 

5.253349 

35 

4.866749 

5.074461 

5.290784 

5.516015 

36 

5.091836 

5.315500 

5.548710 

5.791816 

37 

5.327332 

5.567985 

5.819210 

6.081406 

38 

5.573720 

5.832464 

6.102896 

6.385476 

39 

5.831504 

6.109504 

6.400413 

6.704750 

40 

6.101210 

6.399706 

6.712433 

7.039988 

41 

6.383390 

6.703690 

7.039665 

7.391987 

42 

6.678621 

7.022117 

7.382848 

7.761587 

43 

6.987506 

7.355667 

7.742764 

8.149666 

44 

7.310677 

7.705060 

8.120224 

8.557150 

45 

7.648795 

8.071050 

8.516084 

8.985008 

46 

8.002550 

8.454424 

8.931244 

9.434258 

47 

8.372668 

8.856008 

9.366644 

9.905971 

48 

8.759902 

9.276669 

9.823269 

10.40127 

49 

9.165044 

9.717309 

10.30215 

10.92133 

50 

9.588927 

10.17888 

10.80436 

11.46740 


35 




Rale, 4%% lo 5% 
Years, 51 to 75 


TABLE I 

COMPOUND INTEREST 


The value of $1 invested at a fixed rate of compound interest for one 
to one hundred years. 


Years 

4%% 

4%% 

4%% 

5% 

51 

10.00934 

10.66238 

11.33110 

12.04077 

52 

10.47227 

11.16884 

11.88349 

12.64281 

53 

10.98187 

11.69936 

12.46281 

13.27495 

54 

11.48978 

12.25508 

13.07037 

13.93869 

55 

12.02118 

12.83719 

13.70755 

14.63563 

56 

12.57715 

13.44696 

14.37580 

15.36741 

57 

13.15885 

14.08568 

15.07662 

16.13578 

58 

13.76744 

14.75475 

15.81161 

16.94259 

59 

14.40418 

15.45560 

16.58242 

17.78970 

60 

15.07037 

16.18975 

17.43091 

18.67919 

61 

15.76737 

16.95876 

18.23862 

19.61315 

62 

16.49661 

17.76430 

19.12775 

20.59381 

63 

17.25958 

18.60810 

20.06024 

21.62350 

64 

18.05783 

19.49198 

21.03817 

22.70467 

65 

18.89300 

20.41785 

22.06379 

23.83990 

66 

19.76680 

21.38769 

23.13940 

25.03190 

67 

20.68101 

22.40361 

24.26744 

26.28349 

68 

21.63750 

23.46778 

25.45048 

27.59766 

69 

22.63824 

24.58250 

26.69120 

28.97754 

70 

23.68525 

25.75017 

27.99239 

30.42642 

71 

24.78069 

26.97329 

29.35702 

31.94774 

72 

25.92679 

28.25453 

30.78818 

33.54513 

73 

27.12590 

29.59661 

32.28911 

35.22238 

74 

28.38047 

31.00245 

33.86320 

36.98350 

75 

29.69306 

32.47506 

35.51403 

38.83269 


36 





TABLE I 

COMPOUND INTEREST 


Rate. 4 %% to 5% 
Years, 76 to 100 


The value of $1 invested at a fixed rate of compound interest for one, 
to one hundred years. 


Years 

4%% 

4%% 

4%% 

5% 

76 

31.06636 

34.01762 

37.24534 

40.77432 

77 

32.50318 

35.63346 

39.06105 

42.81304 

78 

34.00644 

37.32604 

40.96528 

44.95369 

79 

35.57924 

39.09905 

42.96235 

47.20138 

80 

37.22477 

40.95624 

45.05676 

49.56144 

81 

38.94641 

42.90165 

47.25329 

52.03951 

82 

40.74767 

44.93947 

49.55689 

54.64149 

83 

42.63225 

47.07410 

51.97278 

57.37356 

84 

44.60398 

49.31011 

54.50646 

60.24224 

85 

46.66690 

51.65233 

57.16365 

63.25435 

86 

48.82523 

54.10583 

59.95038 

66.41707 

87 

51.08340 

56.67584 

62.87297 

69.73792 

88 

53.44600 

59.36794 

65.93803 

73.22482 

89 

55.91786 

62.18791 

69.15252 

76.88607 

90 

58.50405 

65.14183 

72.52372 

80.73037 

91 

61.20986 

68.23606 

76.05925 

84.76689 

92 

64.04081 

71.47728 

79.76714 

89.00523 

93 

67.00269 

74.87245 

83.65579 

93.45549 

94 

70.10155 

78.42887 

87.73402 

98.12826 

95 

73.34373 

82.15424 

92.01104 

103.0347 

96 

76.73585 

86.05656 

96.49660 

108.1864 

97 

80.28489 

90.14424 

101.2008 

113.5957 

98 

83.99766 

94.42609 

106.1343 

119.2755 

99 

87.88294 

98.91132 

111.3084 

125.2393 

100 

91.94750 

103.6096 

116.7347 

131.5012 


37 




Rate, S^^toSi/jJo" 

Years 1 to 25 


TABLE I 

COMPOUND INTEREST 


The value of $1 invested at a fixed rate of compound interest for one 
to one hundred years. 


Years 


5%% 

5%% 

5V2(fo 

1 

1.051250 

1.052500 

1.053750 

1.055000 

2 

1.105127 

1.107756 

1.110389 

1.113025 

3 

1.161765 

1.165913 

1.170072 

1.174241 

4 

1.221306 

1.227124 

1.232964 

1.238824 

5 

1.283898 

1.291548 

1.299236 

1.306960 

6 

1.349698 

1.359354 

1.369070 

1.378843 

7 

1.418870 

1.430720 

1.442658 

1.454680 

8 

1.491588 

1.505833 

1.520200 

1.534687 

9 

1.568032 

1.584889 

1.601911 

1.619095 

10 

1.648394 

1.668096 

1.688914 

1.708145 

11 

1.732875 

1.755671 

1.774654 

1.802094 

12 

1.821685 

1.847844 

1.874352 

1.901209 

13 

1.915046 

1.944856 

1.975099 

2.005776 

14 

2.013193 

2.046961 

2.081260 

2.116093 

IS 

2.116370 

2.154426 

2.193128 

2.232479 

16 

2.224834 

2.267533 

2.311009 

2.355266 

17 

2.338857 

2.386579 

2.435226 

2.484806 

18 

2.458724 

2.511874 

2.566119 

2.621470 

19 

2.584735 

2.643748 

2.704048 

2.765651 

20 

2.717202 

2.782544 

2.849391 

2.917763 

21 

2.856460 

2.928628 

3.002545 

3.078240 

22 

3.002833 

3.082381 

3.163933 

3.247543 

23 

3.156751 

3.244206 

3.333994 

3.426158 

24 

3.318535 

3.414526 

3.513196 

3.614597 

23 

3.488611 

3.593788 

3.702031 

3.813400 


38 





TABLE I 


Rate, 5ys%lo5M!% 
Years, 26 to 50 


COMPOUND INTEREST 


The value of $1 invested at a fixed rate of compound interest for one 
to one hundred years. 


Years 

51 / 8 % 

5V0O 

5%fo 


26 

3.667403 

3.782462 

3.901016 

4.023137 

27 

3.855358 

3.981041 

4.110695 

4.244410 

28 

4.052946 

4.190046 

4.331645 

4.477853 

29 

4.260660 

4.410023 

4.564470 

4.724136 

30 

4.479020 

4.641550 

4.809811 

4.983965 

31 

4.708571 

4.885231 

5.068338 

5.258083- 

32 

4.949886 

5.141706 

5.340761 

5.547278 

33 

5.203568 

5.411645 

5.627828 

5.852379 

34 

5.470253 

5.695756 

5.930323 

6.174261 

35 

5.750604 

5.994782 

6.249079 

6.513846 

36 

6.045324 

6.309508 

6.584966 

6.872108 

37 

6.355149 

6.640757 

6.940506 

7.250075 

38 

6.674700 

6.989397 

7.311877 

7.648830 

39 

7.023246 

7.356341 

7.704890 

8.069517 

40 

7.383190 

7.742550 

8.119027 

8.513342 

41 

7.761579 

8.149033 

8.555426 

8.981576 

42 

8.159362 

8.576857 

9.015280 

9.475563 

43 

8.577532 

9.027142 

9.499850 

9.996719 

44 

9.017132 

9.501067 

10.01047 

10.54654 

45 

9.479260 

9.999872 

10.54853 

11.12660 

46 

9.965074 

10.52487 

11.11552 

11.73857 

47 

10.47579 

11.07742 

11.71298 

12.38419 

48 

11.01268 

11.65898 

12.34255 

13.06532 

49 

11.57708 

12.27108 

13.00596 

13.78392 

50 

12.17040 

12.91531 

39 

13.70503 

14.54203 




Rale, SMXtoSViX 
Years, 51 to 75 


TABLE I 


COMPOUND INTEREST 


The value of $1 invested at a fixed rate of componnd interest for one 
to one hundred years. 


Years 

5%% 

51 / 4 % 

5%% 

5%9'o 

51 

12.79414 

13.59336 

14.44168 

15.34184 

52 

13.44984 

14.30701 

15.21792 

16.18565 

53 

14.13915 

15.05813 

16.03588 

17.07586 

54 

14.86379 

15.84869 

16.89781 

18.01504 

55 

15.62556 

16.68075 

17.80607 

19.00586 

56 

16.46423 

17.55649 

18.76314 

20.05118 

57 

17.26823 

18.47820 

19.77166 

21.15400 

58 

18.15322 

19.44831 

20.83439 

22.31747 

59 

19.08358 

20.46934 

21.95424 

23.54493 

60 

20.06162 

21.54398 

23.13428 

24.83990 

61 

21.08978 

22.67504 

24.37775 

26.20610 

62 

22.17064 

23.86548 

25.68805 

27.64744 

63 

23.30689 

25.11841 

27.06879 

29.16805 

64 

24.50137 

26.43713 

28.52374 

30.77230 

65 

25.75707 

27.82508 

30.05689 

32.46478 

66 

27.07713 

29.28590 

31.67144 

34.25035 

67 

28.46484 

30.82341 

33.37484 

36.13412 

68 

29.92367 

32.44164 

35.16874 

38.12149 

69 

31.45726 

34.14482 

37.05906 

40.21819 

70 

33.06945 

35.93743 

39.05098 

42.43019 

71 

34.76427 

37.82415 

41.14998 

44.76386 

72 

36.54595 

39.80992 

43.36179 

47.22588 

73 

38.41893 

41.89994 

45.69248 

49.82330 

74 

40.38792 

44.09968 

48.14846 

52.56359 

75 

42.45780 

46.41490 

50.73645 

55.45459 


40 





TABLE 1 


Rate, SVs^ to 51/25^ 

Year*, 76 to 100 


COMPOUND INTEREST 


The value of $1 invested at a fixed rate of compound interest for one 
to one hundred years. 


Years 

5V8<fo 

5%% 

5%% 

51 / 2 % 

76 

44.63377 

48.85168 

53.46845 

58.50460 

77 

46.92127 

51.41640 

56.33720 

61.72236 

78 

49.32599 

54.11576 

59.36631 

65.11708 

79 

55.85395 

56.95684 

62.55620 

68.69854 

80 

54.51149 

59.94707 

65.91860 

72.47696 

81 

57.30521 

63.09429 

69.46173 

76.46320 

82 

60.94211 

66.40674 

73.19530 

80.66868 

83 

63.32953 

69.89310 

77.12955 

85.10547 

84 

66.57518 

73.56248 

81.27526 

89.78628 

85 

69.98718 

77.42452 

85.64382 

94.72454 

86 

73.57403 

81.48931 

90.24716 

99.93439 

87 

77.34474 

85.76750 

95.09799 

105.4308 

88 

81.30866 

90.27029 

100.2095 

111.2295 

89 

85.47574 

95.00948 

105.5957 

117.3471 

90 

89.85640 

99.99747 

111.2715 

123.8012 

91 

94.46156 

105.2473 

117.2524 

130.6103 

92 

99.30272 

110.7728 

123.5547 

137.7938 

93 

104.3920 

116.5884 

130.1958 

145.3725 

94 

109.7421 

122.7093 

137.1938 

153.3680 

95 

115.3665 

129.1515 

144.5680 

161.8033 

96 

121.2790 

135.9320 

152.3385 

170.7025 

97 

127.4946 

143.0684 

160.5267 

180.0912 

98 

134.0287 

150.5795 

169.1550 

189.9962 

99 

140.8977 

158.4849 

178.2471 

200.4459 

100 

148.1188 

166.8053 

187.8279 

211.4705 


41 




Rate, 5%% to e% 
Years, 1 to 25 


TABLE I 

COMPOUND INTEREST 


The value of $1 invested at a fixed rate 
to one hundred years. 

of compound 

interest for one 

Years 

5%% 

5%% 

5%% 

6% 

1 

1.056250 

1.057500 

1.058750 

1.060000 

2 

1.115639 

1.118306 

1.120951 

1.123600 

3 

1.178421 

1.182609 

1.186807 

1.191016 

4 

1.244707 

1.250609 

1.256532 

1.262476 

S 

1.314722 

1.322519 

1.330353 

1.338225 

6 

1.388676 

1.398564 

1.408511 

1.418520 

7 

1.466789 

1.478982 

1.491261 

1.503631 

8 

1.549296 

1.564023 

1.578873 

1.593849 

9 

1.636444 

1.653955 

1.671631 

1.689480 

10 

1.728494 

1.749057 

1.769840 

1.790849 

11 

1.825723 

1.849628 

1.873818 

1.898300 

12 

1.928420 

1.955982 

1.983905 

2.012198 

13 

2.036894 

2.068451 

2.100459 

2.132930 

14 

2.151469 

2.187389 

2.223860 

2.260906 

15 

2.272490 

2.313162 

2.354513 

2.396561 

16 

2.400318 

2.446178 

2.492840 

2.540355 

17 

2.535336 

2.586833 

2.639294 

2.692776 

18 

2.677949 

2.735566 

2.794353 

2.854343 

19 

2.828585 

2.892861 

2.958521 

3.025604 

20 

2.987693 

3.059201 

3.132334 

3.207140 

21 

3.155751 

3.235105 

3.316358 

3.399568 

22 

3.333263 

3.421124 

3.511193 

3.603543 

23 

3.520760 

3.617838 

3.717476 

3.819755 

24 

3.718803 

3.825864 

3.935879 

4.048941 

25 

3.927986 

4.045852 

4.167111 

4.291879 


42 




TABLE I 


Rate, 5%% to 6%” 
Years, 26 to 50 


COMPOUND INTEREST 


The value of $1 invested at a fixed rate of compound interest for one 
to one hundred years. 


Years 

5%% 

5%% 

5%% 

6% 

26 

4.148937 

4.278489 

4.411927 

4.549392 

27 

4.382315 

4.524502 

4.671128 

4.822356 

28 

4.628821 

4.784661 

4.945557 

5.111698 

29 

4.889193 

5.059779 

5.236108 

5.418401 

30 

5.164211 

5.350717 

5.543729 

5.743505 

31 

5.454700 

5.658384 

5.869423 

6.088115 

32 

5.761527 

5.983741 

6.214251 

6.453402 

33 

6.085614 

6.327807 

6.579338 

6.840606 

34 

6.427931 

6.691655 

6.965875 

7.251043 

35 

6.789503 

7.076427 

7.375119 

7.686105 

36 

7.171415 

7.483330 

7.808405 

8.147271 

37 

7.574807 

7.913612 

8.267150 

8.636108 

38 

8.000892 

8.368646 

8.752844 

9.154274 

39 

8.450944 

8.849842 

9.267074 

9.703531 

40 

8.926310 

9.358710 

9.811515 

10.28575 

41 

9.428417 

9.896837 

10.38794 

10.90290 

42 

9.958769 

10.46591 

10.99823 

11.55707 

43 

10.51895 

11.06769 

11.64438 

12.25050 

44 

11.11064 

11.70409 

12.32848 

12.98553 

45 

11.73562 

12.37707 

13.05278 

13.76466 

46 

12.39575 

13.08876 

13.81963 

14.59054 

47 

13.09301 

13.84136 

14.63153 

15.46597 

48 

13.82950 

14.63724 

15.49113 

16.39394 

49 

14.60741 

15.47888 

16.40124 

17.37787 

50 

15.42908 

16.36892 

17.36481 

18.42023 


43 




Rate, 5%X *<> 
Years, 51 to 75 


TABLE I 

COMPOUND INTEREST 


The value of $1 invested at a fixed rate of compound interest for one 
to one hundred years. 


Years 

5%% 

5%% 

5%% 

6% 

51 

16.29697 

17.31013 

18.34499 

19.52544 

52 

17.21367 

18.30547 

19.46511 

20.69597 

53 

18.18195 

19.35803 

20.60868 

21.93878 

54 

19.20468 

20.47112 

21.81944 

23.25511 

55 

20.28495 

21.64821 

23.10133 

24.65042 

56 

21.42598 

22.89298 

24.45853 

26.12945 

57 

22.63120 

24.20933 

25.89547 

27.69722 

58 

23.90421 

25.60137 

27.41683 

29.35905 

59 

25.24882 

27.07345 

29.02756 

31.12060 

60 

26.66908 

28.63018 

30.73293 

32.98784 

61 

28.16922 

30.27641 

32.53849 

34.96711 

62 

29.75374 

32.01731 

34.45012 

37.06514 

63 

31.42740 

33.85831 

36.47407 

39.28905 

64 

33.19519 

35.80516 

38.61692 

41.64640 

65 

35.06242 

37.86395 

40.88566 

44.14519 

66 

37.03470 

40.04114 

43.28769 

46.79390 

67 

39.11791 

42.34350 

45.83084 

49.60154 

68 

41.31829 

44.77826 

48.52340 

52.59764 

69 

43.64246 

47.35301 

51.37415 

55.73230 

70 

46.09735 

50.07581 

54.39238 

59.07625 

71 

58.69033 

52.95517 

57.58791 

62.62084 

72 

51.42918 

56.00010 

60.97121 

66.37809 

73 

54.32208 

59.22011 

64.55326 

70.36079 

74 

57.37771 

62.62527 

68.34576 

74.58244 

75 

60.60521 

66.22623 

72.36107 

79.05740 


44 




TABLE I 


Rate, 5%%to6% 
Years, 76 to 100 


COMPOUND INTEREST 


The value of $1 invested at a fixed rate of compound interest for one 
to one hundred years. 


Years 

5%% 

5%% 

5%% 

6% 

76 

64.01427 

70.03425 

76.61229 

83.80085 

77 

67.61508 

74.06120 

81.11324 

88.82890 

78 

71.41845 

78.31974 

85.87864 

94.15865 

79 

75.43573 

82.82312 

90.92402 

99.80817 

80 

79.67902 

87.58546 

96.26580 

105.7966 

81 

84.16098 

92.62162 

101.9214 

112.1444 

82 

88.89506 

97.94737 

107.9093 

118.8731 

83 

93.89542 

103.5793 

114.2491 

126.0054 

84 

99.17705 

109.5352 

120.9611 

133.5658 

85 

104.7558 

115.8334 

128.0675 

141.5798 

86 

110.6483 

122.4939 

135.5915 

150.0746 

87 

116.8723 

129.5373 

143.5575 

159.0791 

88 

123.4464 

136.9857 

151.9914 

168.6239 

89 

130.3903 

144.8624 

160.9210 

178.7413 

90 

137.7248 

153.1920 

170.3750 

189.4658 

91 

145.4718 

162.0005 

180.3846 

200.8338 

92 

153.6546 

171.3155 

190.9822 

212.8838 

93 

162.2977 

181.1662 

202.2023 

225.6569 

94 

171.4270 

191.5833 

214.0817 

239.1963 

95 

181.0698 

202.5993 

226.6590 

253.5481 

96 

191.2550 

214.2488 

239.9752 

268.7610 

97 

202.0131 

226.5681 

254.0738 

284.8867 

98 

213.3764 

239.5958 

269.0006 

301.9799 

99 

225.3789 

253.3726 

284.8043 

320.0987 

100 

238.0565 

267.9415 

301.5366 

339.3047 


45 





Rate, 6MXto 7% 
Years, 1 to 25 


TABLE I 


COMPOUND INTEREST 


The value of $1 invested at a fixed rate of compound interest for one 
to one hundred years. 


Years 



6%% 

7^0 

1 

1.062500 

1.065000 

1.067500 

1.070000 

2 

1.128906 

1.134225 

1.139556 

1.144900 

3 

1.199463 

1.207949 

1.216476 

1.225043 

4 

1.274429 

1.286466 

1.298588 

1.310796 

5 

1.354081 

1.370086 

1.386243 

1.402551 

6 

1.438711 

1.459142 

1.479814 

1.500730 

7 

1.528631 

1.553986 

1.579702 

1.605781 

8 

1.624170 

1.654995 

1.686332 

1.718187 

9 

1.725680 

1.762570 

1.800160 

1.838460 

10 

1.833534 

1.877136 

1.921671 

1.967152 

11 

1.948130 

1.999150 

2.051383 

2.104853 

12 

2.069888 

2.129095 

2.189852 

2.252192 

13 

2.199256 

2.267486 

2.337667 

2.409846 

14 

2.336709 

2.414873 

2.495460 

2.578535 

15 

2.482753 

2.571840 

2.663904 

2.759033 

16 

2.637925 

2.739010 

2.843717 

2.952166 

17 

2.802795 

2.917046 

3.035668 

3.158818 

18 

2.977970 

3.106654 

3.240576 

3.379935 

19 

3.164093 

3.308586 

3.459315 

3.616531 

20 

3.361847 

3.523644 

3.692819 

3.869688 

21 

3.571962 

3.752681 

3.942084 

4.140566 

22 

3.795210 

3.996605 

4.208175 

4.430406 

23 

4.032410 

4.256384 

4.492227 

4.740535 

24 

4.284435 

4.533048 

4.795453 

5.072373 

25 

4.552212 

4.827696 

5.119146 

5.427440 


46 





TABLE I 

COMPOUND INTEREST 


Rate, 61/4% to 7% 
Years, 26 to 50 


The value of $1 invested at a fixed rate of compound interest for one 
to one hundred years. 


Years 




7^0 

26 

4.836725 

5.141496 

5.464688 

5.807361 

27 

5.139020 

5.475695 

5.833554 

6.213876 

28 

5.460208 

5.831615 

6.227320 

6.648848 

29 

5.801471 

6.210669 

6.647665 

7.114267 

30 

6.164061 

6.614361 

7.096382 

7.612266 

31 

6.549315 

7.044295 

7.575387 

8.145125 

32 

6.958647 

7.502174 

8.086726 

8.715283 

33 

7.393562 

7.989816 

8.632581 

9.325353 

34 

7.855659 

8.509155 

9.215280 

9.978127 

35 

8.346636 

9.062250 

9.837314 

10.67660 

36 

8.868301 

9.651296 

10.50133 

11.42396 

37 

9.422570 

10.27863 

11.21017 

12.22364 

38 

10.01148 

10.94674 

11.96685 

13.07930 

39 

10.63719 

11.65828 

12.77462 

13.99485 

40 

11.30202 

12.41606 

13.63691 

14.97449 

41 

12.00840 

13.22130 

14.55740 

16.02271 

42 

12.75892 

14.08261 

15.54003 

17.14429 

43 

13.55635 

14.99798 

16.58898 

18.34440 

44 

14.40362 

15.97285 

17.70874 

19.62851 

45 

15.30384 

17.01180 

18.90408 

21.00251 

46 

16.26034 

18.11680 

20.18010 

22.47268 

47 

17.27661 

19.29440 

21.54226 

24.04577 

48 

18.35640 

20.54854 

22.99636 

25.72897 

49 

19.50367 

21.88419 

24.54862 

27.53000 

50 

20.72264 

23.30666 

26.20565 

29.45710 


47 




Rale, ey^XtoTX 
Years, 51 to 75 


TABLE I 


COMPOUND INTEREST 


The value of $1 invested at a fixed rate of compound interest for one 
to one hundred years. 


Years 

6%% 

6%% 

6%% 

7% 

51 

22.01780 

24.82159 

27.97453 

31.51910 

52 

23.39391 

26.43498 

29.86281 

33.72544 

53 

24.85603 

28.15326 

31.87855 

36.08622 

54 

26.40953 

29.98323 

34.03036 

38.61226 

55 

28.06012 

31.93213 

36.32742 

41.31512 

56 

29.81388 

34.00772 

38.77952 

44.20718 

57 

31.67724 

36.21822 

41.39714 

47.30169 

58 

33.65707 

38.57241 

44.19145 

50.61280 

59 

35.76063 

41.07962 

47.17437 

54.15570 

60 

37.99566 

43.74979 

50.35863 

57.94660 

61 

40.37639 

46.59352 

53.75784 

62.00286 

62 

42.89353 

49.62210 

57.38650 

66.34307 

63 

45.57437 

52.84753 

61.26009 

70.98709 

64 

48.42277 

56.28262 

65.39515 

75.95619 

65 

51.44918 

59.94100 

69.80933 

81.27312 

66 

54.66475 

63.83716 

74.52146 

86.96224 

67 

58.08129 

67.98658 

79.55166 

93.04959 

68 

61.71136 

72.40570 

84.92140 

99.56307 

69 

65.56832 

77.11207 

90.65360 

106.5325 

70 

69.66633 

82.12435 

96.77272 

113.9897 

71 

74.02047 

87.46244 

103.3048 

121.9691 

72 

78.64674 

93.14750 

110.2780 

130.5069 

73 

83.56216 

99.20198 

117.7217 

139.6424 

74 

88.78479 

105.6501 

125.6679 

149.4174 

75 

94.33382 

112.5174 

48 

134.1505 

159.8766 




TABLE I 


R«te, 6%% to 7% 
Yean, 76 to 100 


COMPOUND INTEREST 


The value of $1 invested at a fixed rate of compound interest for one 
to one hundred years. 


Years 




7% 

76 

100.2297 

119.8311 

143.2056 

171.0680 

77 

106.4940 

127.6201 

152.8720 

183.0428 

78 

113.1498 

135.9154 

163.1909 

195.8558 

79 

120.2217 

144.7499 

174.2063 

209.5657 

80 

127.7356 

154.1586 

185.9653 

224.2353 

81 

135.7191 

164.1789 

198.5180 

239.9318 

82 

144.2015 

174.8506 

211.9181 

256.7271 

83 

153.2141 

186.2159 

226.2225 

274.6980 

84 

162.7899 

198.3199 

241.4925 

293.9268 

85 

172.9643 

211.2107 

257.7932 

314.5017 

86 

183.7745 

224.9394 

275.1943 

336.5169 

87 

195.2604 

239.5606 

293.7699 

360.0731 

88 

207.4642 

255.1320 

313.5994 

385.2782 

89 

220.4307 

271.7155 

334.7674 

412.2477 

90 

234.2076 

289.3770 

357.3642 

441.1050 

91 

248.8456 

308.1865 

381.4863 

471.9824 

92 

264.3984 

328.2186 

407.2366 

505.0212 

93 

280.9233 

349.5528 

434.7251 

540.3727 

94 

298.4810 

372.2737 

464.0689 

578.1988 

95 

317.1360 

396.4715 

495.3938 

618.6727 

96 

336.9570 

422.2421 

528.8329 

661.9798 

97 

358.0168 

449.6878 

564.5291 

708.3185 

98 

380.3928 

478.9176 

602.6348 

757.9008 

99 

404.1673 

510.0472 

643.3127 

810.9540 

100 

429.4276 

543.2002 

686.7363 

867.7208 


9 

49 






Rate. 71 / 4 % to S}i 
Year*. 1 to 25 


TABLE I 


COMPOUND INTEREST 


The value of $1 invested at a fixed rate 
to one hundred years. 

of compound 

interest for one 

Years 

71 / 4 % 

7%% 

7 %% 

8% 

1 

1.072500 

1.075000 

1.077500 

1.080000 

2 

1.150256 

1.155625 

1.161006 

1.166400 

3 

1.233649 

1.242296 

1.250984 

1.259712 

4 

1.323089 

1.335469 

1.347935 

1.360489 

5 

1.419013 

1.435629 

1.452401 

1.469328 

6 

1.521891 

1.543302 

1.564962 

1.586875 

7 

1.632228 

1.659050 

1.686247 

1.713825 

8 

1.730565 

1.783479 

1.816931 

1.850931 

9 

1.877481 

1.917240 

1.957743 

1.999006 

10 

2.013599 

2.061033 

2.109468 

2.158927 

11 

2.159585 

2.215610 

2.272952 

2.331641 

12 

2.316155 

2.381781 

2.449107 

2.518173 

13 

2.484076 

2.560415 

2.638913 

2.719627 

14 

2.664172 

2.752447 

2.843428 

2.937198 

15 

2.857325 

2.958880 

3.063793 

3.172173 

16 

3.064481 

3.180797 

3.301237 

3.425947 

17 

3.286656 

3.419357 

3.557083 

3.700023 

18 

3.524938 

3.675809 

3.832757 

3.996025 

19 

3.780496 

3.951495 

4.129796 

4.315707 

20 

4.054581 

4.247857 

4.449856 

4.660966 

21 

4.348538 

4.566447 

4.794720 

5.033843 

22 

4.663807 

4.908931 

5.166311 

5.436552 

23 

5.001933 

5.277101 

5.566701 

5.871476 

24 

5.364573 

5.672884 

5.998121 

6.341195 

23 

5.753505 

6.098351 

6.462976 

6.848491 


50 





TABLE I 

COMPOUND INTEREST 


Rale, 714% to 8% 
Yeara, 26 to 50 


The value of $1 invested at a fixed rate of compound interest for one 
to one hundred years. 


Years 

7%% 

7y2% 

7%fo 

8 % 

26 

6.170634 

6.555729 

6.963857 

7.396370 

27 

6.618005 

7.047409 

7.503556 

7.988080 

28 

7.097810 

7.575965 

8.085081 

8.627126 

29 

7.612401 

8.144163 

8.711675 

9.317296 

30 

8.164300 

8.754976 

9.386830 

10.06268 

31 

8.756212 

9.411600 

10.11431 

10.86770 

32 

9.391037 

10.11747 

10.89817 

11.73711 

33 

10.07189 

10.87628 

11.74278 

12.67608 

34 

10.80210 

11.69200 

12.65284 

13.69017 

35 

11.58525 

12.56890 

13.63344 

14.78539 

36 

12.42518 

13.51157 

14.69003 

15.96823 

37 

13.32600 

14.52494 

15.82851 

17.24568 

38 

14.29216 

15.61431 

17.05522 

18.62534 

39 

15.32834 

16.78539 

18.37700 

20.11538 

40 

16.43963 

18.04430 

19.80122 

21.72461 

41 

17.63150 

19.39762 

1.233581 

23.46258 

42 

18.90978 

20.85244 

22.98934 

25.33959 

43 

20.28074 

22.41638 

24.77101 

27.36676 

44 

21.75109 

24.09761 

26.69077 

29.55610 

45 

23.32805 

25.90493 

28.75931 

31.92059 

46 

25.01933 

27.84780 

30.98816 

34.47424 

47 

26.83323 

29.93638 

33.38974 

37.23218 

48 

28.77865 

32.18163 

35.97745 

40.21076 

49 

30.86510 

34.59525 

38.76570 

43.42763 

50 

33.10282 

37.18990 

41.77005 

46.90185 


51 




Rate, 71 / 4 % to 8% 
Years, 51 to 75 


TABLE I 


COMPOUND INTEREST 


The value of $1 invested at a fixed rate of compound interest for one 
to one hundred years. 


Years 

7Vi<^o 

7 V 20/0 

7%% 

8% 

51 

35.50277 

39.97914 

45.00723 

50.65400 

52 

38.07672 

42.97758 

48.49529 

54.70632 

53 

40.83728 

46.20090 

52.25368 

59.08283 

54 

43.79798 

49.66597 

56.30335 

63.80946 

55 

46.97334 

53.39092 

60.66686 

68.91423 

56 

50.37891 

57.39524 

65.36854 

74.42737 

57 

54.03138 

61.69989 

70.43461 

80.38156 

58 

57.94866 

66.32740 

75.89330 

86.81209 

59 

62.14994 

71.30196 

81.77503 

93.75706 

60 

66.65581 

76.64961 

88.11260 

101.2577 

61 

71.48836 

82.39834 

94.94133 

109.3583 

62 

76.67127 

88.57822 

102.2993 

118.1070 

63 

82.22993 

95.22160 

110.2275 

127.5556 

64 

88.19160 

102.3632 

118.7701 

137.7600 

65 

94.58549 

110.0404 

127.9748 

148.7808 

66 

101.4429 

118.2935 

137.8929 

160.6833 

67 

108.7975 

127.1655 

148.5796 

173.5380 

68 

116.6853 

136.7029 

160.0945 

187.4211 

69 

125.1450 

146.9557 

172.5018 

202.4148 

70 

134.2181 

157.9774 

185.8707 

218.6080 

71 

143.9489 

169.8257 

200.2757 

236.0967 

72 

154.3852 

182.5627 

215.7971 

254.9844 

73 

165.5781 

196.2549 

232.5214 

275.3832 

74 

177.5825 

210.9741 

250.5418 

297.4139 

75 

190.4572 

226.7971 

269.9588 

321.2070 


52 




TABLE I 


Rate, 71 / 4 ^ to 8X 
Year*, 76 to 100 


COMPOUND INTEREST 

The value of $1 invested at a fixed rate of compound interest for one 
to one hundred years. 


Years 

71 / 4 % 

71 / 2 % 

7%% 

8fo 

76 

204.2654 

243.8069 

290.8806 

346.9036 

77 

219.0746 

262.0924 

313.4239 

374.6559 

78 

234.9575 

281.7494 

337.7143 

404.6283 

79 

251.9920 

302.8806 

363.8871 

436.9986 

80 

270.2614 

325.5966 

392.0884 

471.9585 

81 

289.8554 

350.0164 

422.4753 

509.7152 

82 

310.8699 

376.2677 

455.2171 

550.4925 

83 

333.4079 

404.4878 

490.4964 

594.5320 

84 

357.5800 

434.8244 

528.5099 

642.0947 

85 

383.5045 

467.4363 

569.4695 

693.4624 

86 

411.3086 

502.4941 

613.6034 

748.9394 

87 

441.1285 

540.1812 

661.1577 

808.8546 

88 

473.1103 

580.6948 

712.3975 

873.5630 

89 

507.4108 

624.2470 

767.6084 

943.4480 

90 

544.1981 

671.0656 

827.0980 

1018.924 

91 

583.6525 

721.3956 

891.1981 

1100.438 

92 

625.9673 

775.5004 

960.2660 

1188.473 

93 

671.3499 

833.6630 

1034.687 

1283.551 

94 

720.0227 

896.1878 

1114.875 

1386.235 

95 

772.2243 

963.4020 

1201.278 

1497.134 

96 

828.2106 

1035.657 

1294.377 

1616.905 

97 

888.2558 

1113.331 

1394.691 

1746.258 

98 

952.6543 

1196.831 

1502.780 

1885.959 

99 

1021.722 

1286.593 

1619.246 

2036.836 

100 

1095.797 

1383.088 

1744.737 

2199.783 


53 




Rate, S},i% to 9% 
Years, 1 to 25 


TABLE I 


COMPOUND INTEREST 

The value of $1 invested at a fixed rate of compound interest for one 
to one hundred years. 


Years 

81/4% 

81/2% 

8 %% 

9% 

1 

1.082500 

1.085000 

1.087500 

1.090000 

2 

1.171806 

1.177225 

1.182656 

1.188100 

3 

1.268480 

1.277289 

1.286139 

1.295029 

4 

1.373130 

1.385858 

1.398676 

1.411581 

5 

1.486413 

1.503656 

1.521060 

1.538623 

6 

1.609042 

1.631466 

1.654153 

1.677100 

7 

1.741788 

1.770141 

1.798892 

1.828039 

8 

1.885486 

1.920603 

1.956295 

1.992562 

9 

2.041038 

2.083853 

2.127471 

2.171893 

10 

2.209424 

2.260981 

2.313625 

2.367363 

11 

2.391702 

2.453164 

2.516067 

2.580426 

12 

2.589017 

2.661683 

2.736223 

2.812665 

13 

2.802611 

2.887926 

2.975643 

3.065804 

14 

3.033826 

3.133400 

3.236012 

3.341726 

15 

3.284116 

3.399738 

3.519164 

3.642482 

16 

3.555055 

3.688716 

3.827091 

3.970305 

17 

3.848347 

4.002256 

4.161961 

4.327633 

18 

4.165836 

4.342448 

4.526133 

4.717120 

19 

4.509517 

4.711556 

4.922170 

5.141661 

20 

4.881552 

5.112037 

5.352861 

5.604411 

21 

5.284280 

5.546560 

5.821237 

6.108808 

22 

5.720233 

6.018017 

6.330595 

6.658601 

23 

6.192152 

6.529549 

6.884523 

7.257875 

24 

6.703005 

7.084560 

7.486919 

7.911084 

25 

7.256003 

7.686745 

8.142026 

8.623082 


64 




TABLE I 


Rale, 8%% to 9% 
Years, US to 50 


COMPOUND INTEREST 


The value of $1 invested at a fixed rate of compound interest for one 
to one hundred years. 


Years 

8^/4% 

81/2% 

8 %% 

9% 

26 

7.854623 

8.340119 

8.854453 

9.399160 

27 

8.502629 

9.049029 

9.629218 

10.24808 

28 

9.204096 

9.818197 

10.47177 

11.16714 

29 

9.963434 

10.65274 

11.38806 

12.17218 

30 

10.78542 

11.55822 

12.38452 

13.26767 

31 

11.67522 

12.54067 

13.46817 

14.46176 

32 

12.63842 

13.60663 

14.64663 

15.76332 

33 

13.68109 

14.76318 

15.92821 

17.18202 

34 

14.80978 

16.01805 

17.32193 

18.72841 

35 

16.03158 

17.37958 

18.83759 

20.41397 

36 

17.35419 

18.85685 

20.48588 

22.25123 

37 

18.78591 

20.45968 

22.27841 

24.25383 

38 

20.33575 

22.19875 

24.22777 

26.43668 

39 , 

22.01345 

24.08564 

26.34770 

28.81598 

40 

23.82956 

26.13292 

28.65313 

31.40942 

41 

25.79550 

28.35422 

31.16028 

34.23627 

42 

27.92362 

30.76432 

33.88681 

37.31754 

43 

30.22732 

33.37928 

36.85190 

40.67612 

44 

30.72107 

36.21652 

40.07645 

44.33697 

45 

35.42056 

39.29492 

43.58314 

48.32730 

46 

38.34276 

42.63499 

47.39667 

52.67676 

47 

41.50604 

46.25896 

51.54388 

57.41765 

48 

44.93028 

50.19097 

56.05397 

62.58525 

49 

48.63703 

54.45719 

60.95870 

68.21792 

50 

52.64958 

59.08605 

66.29259 

74.35753 


55 





Rate, 81/4^10 9% 
Years, 51 to 75 


TABLE I 


COMPOUND INTEREST 

The value of $1 invested at a fixed rate of compound interest for one 
to one hundred years. 


Years 

8 %% 

8 ^2% 

8 %% 

9% 

51 

56.99317 

64.10836 

72.09319 

81.04971 

52 

61.69511 

69.55756 

78.40134 

88.34418 

53 

66.78496 

75.46995 

85.26146 

96.29516 

54 

72.29472 

81.88489 

92.72184 

104.9617 

55 

78.25904 

88.84510 

100.8350 

114.4083 

56 

84.71541 

96.39693 

109.6581 

124.7050 

57 

91.70443 

104.5906 

119.2532 

135.9285 

58 

99.27005 

113.4808 

129.6879 

148.1620 

59 

107.4598 

123.1267 

141.0356 

161.4966 

60 

116.3252 

133.5924 

153.3762 

176.0313 

61 

125.9220 

144.9478 

166.7966 

191.8741 

62 

136.3106 

157.2684 

181.3913 

209.1429 

63 

147.5563 

170.6362 

197.2631 

227.9658 

64 

159.7297 

185.1402 

214.5237 

248.4827 

65 

172.9074 

200.8771 

233.2945 

270.8461 

66 

187.1723 

217.9516 

253.7078 

295.2223 

67 

202.6140 

236.4775 

275.9073 

321.7922 

68 

219.3296 

256.5781 

300.0492 

350.7535 

69 

237.4243 

278.3872 

326.3035 

382.3213 

70 

257.0118 

302.0501 

354.8551 

416.7302 

71 

278.2153 

327.7244 

385.9049 

454.2360 

72 

301.1680 

355.5810 

419.6716 

495.1172 

73 

326.0143 

385.8053 

456.3929 

539.6777 

74 

352.9105 

418.5987 

496.3273 

588.2487 

75 

382.0256 

454.1795 

539.7560 

641.1911. 


56 





TABLE I 


Rate, 81/4% to 9 % 
Years, 76 to 100 


COMPOUND INTEREST 

The value of $1 invested at a fixed rate of compound interest for one 
^0 one hundred years. 


Years 

81/4% 

81/2% 

8%% 

9% 

76 

413.5427 

492.7847 

586.9847 

698.8983 

77 

447.6600 

534.6713 

638.3460 

761.7992 

78 

484.5919 

580.1183 

694.2013 

830.3611 

79 

524.5708 

629.4283 

754.9440 

905.0936 

80 

567.8479 

682.9296 

821.0016 

986.5520 

81 

614.6953 

740.9786 

892.8392 

1075.342 

82 

665.4077 

803.9618 

970.9616 

1172.122 

83 

720.3038 

872.2985 

1056.922 

1277.613 

84 

779.7288 

946.4439 

1148.315 

1392.598 

85 

844.0564 

1026.891 

1248.793 

1517.932 

86 

913.3911 

1114.177 

1358.062 

1654.546 

87 

989.0706 

1208.882 

1476.893 

1803.455 

88 

1070.669 

1311.637 

1606.121 

1965.766 

89 

1158.999 

1423.126 

1746.657 

2142.685 

90 

1254.616 

1544.091 

1899.490 

2335.527 

91 

1358.122 

1675.339 

2065.696 

2545.725 

92 

1470.167 

1817.743 

2246.443 

2774.840 

93 

1591.456 

1972.251 

2443.009 

3024.576 

94 

1722.752 

2139.892 

2656.772 

3296.788 

95 

1864.879 

2321.782 

2889.239 

3593.498 

96 

2018.732 

2519.134 

3142.048 

3916.913 

97 

2185.277 

2733.260 

3416.977 

4269.436 

98 

2365.561 

2965.587 

3715.964 

4653.386 

99 

2560.720 

3217.661 

4041.111 

5072.518 

100 

2771.979 

3491.162 

4394.708 

5529.043 


57 





Rate, 91 / 4 % to 10% 
Years, 1 to 25 


TABLE I 


COMPOUND INTEREST 


The value of $1 invested at a fixed rate of compound interest foi one 
to one hundred years. 


Years 

91 / 4 % 

91 / 2 % 

9%% 

10% 

1 

1.092500 

1.095000 

1.097500 

1.100000 

2 

1.193556 

1.199025 

1.204506 

1.210000 

3 

1.303960 

1.312932 

1.321945 

1.331000 

4 

1.424576 

1.437661 

1.450835 

1.464100 

5 

1.556349 

1.574238 

1.592291 

1.610510 

6 

1.700311 

1.723790 

1.747539 

1.771561 

7 

1.857590 

1.887550 

1.917924 

1.948717 

8 

2.029417 

2.066868 

2.104922 

2.143589 

9 

2.217138 

2.263221 

2.310152 

2.357948 

10 

2.422222 

2.478226 

2.535391 

2.593743 

11 

2.646277 

2.713658 

2.782592 

2.853117 

12 

2.891058 

2.971455 

3.053894 

3.138430 

13 

3.158481 

3.253743 

3.351649 

3.452273 

14 

3.450640 

3.562849 

3.678435 

3.797500 

15 

3.769823 

3.901320 

4.037082 

4.177250 

16 

4.118531 

4.271945 

4.430697 

4.594975 

17 

4.499495 

4.677780 

4.862689 

5.054272 

18 

4.915698 

5.122169 

5.336801 

5.559920 

19 

5.370400 

5.608775 

5.857139 

6.115912 

20 

5.867161 

6.141607 

6.428209 

6.727504 

21 

6.409872 

6.725059 

7.054959 

7.400255 

22 

7.002785 

7.363939 

7.742818 

8.140281 

23 

7.650542 

8.063513 

8.497743 

8.954309 

24 

8.358216 

8.829546 

9.326273 

9.849740 

25 

9.131350 

9.668352 

10.23558 

10.83471 


58 





TABLE I 


Rate, 9MX to 10% 
Years, 26 to 56 


COMPOUND INTEREST 


The value of $1 invested at a fixed rate of compound interest for one 
to one hundred years. 


Years 

9%% 

91 / 2 % 


10% 

26 

9.976000 

10.58685 

11.23355 

11.91818 

27 

10.89878 

11.59260 

12.32882 

13.11000 

28 

11.90692 

12.69389 

13.53088 

14.42100 

29 

13.00830 

13.89981 

14.85014 

15.86310 

30 

14.21157 

15.22029 

16.29803 

17.44942 

31 

15.52614 

16.66622 

17.88709 

19.19436 

32 

16.96231 

18.24951 

19.63108 

21.11380 

33 

18.53132 

19.98322 

21.54511 

23.22519 

34 

20.24546 

21.88162 

23.64575 

25.54771 

35 

22.11816 

23.96037 

25.95121 

28.10248 

36 

24.16409 

26.23660 

28.48145 

30.91273 

37 

26.39925 

28.72908 

31.25838 

34.00400 

38 

28.84119 

31.45833 

34.30607 

37.40440 

39 

31.50900 

34.44687 

37.65092 

41.14483 

40 

34.42358 

37.71932 

41.32188 

45.25931 

41 

37.60776 

41.30266 

45.35076 

49.78524 

42 

41.08647 

45.22641 

49.77245 

54.76377 

43 

44.88696 

49.52292 

54.62526 

60.24014 

44 

49.03901 

54.22759 

59.95122 

66.26416 

45 

53.57510 

59.37921 

65.79646 

72.89057 

46 

58.53079 

65.02023 

72.21161 

80.17963 

47 

63.94489 

71.19715 

79.25224 

88.19759 

48 

69.85978 

77.96088 

86.97933 

97.01735 

49 

76.32180 

85.36716 

95.45981 

106.7191 

50 

83.38156 

93.47704 

104.7671 

117.3910 


59 




Rate, 9y*% to 10% 
Years, 51 to 75 


TABLE I 

COMPOUND INTEREST 


The value of $1 invested at a fixed rate of compound interest for one 
to one hundred years. 


Years 

91 / 4 % 

91 / 2 % 

m°io 

10% 

51 

91.09435 

102.3574 

114.9819 

129.1301 

52 

99.52058 

112.0813 

126.1927 

142.0431 

53 

108.7262 

122.7291 

138.4965 

156.2475 

54 

118.7834 

134.3883 

151.9998 

171.8722 

55 

129.7708 

147.1551 

166.8198 

189.0594 

56 

141.7746 

161.1349 

183.0847 

207.9654 

57 

154.8887 

176.4427 

200.9354 

228.7620 

58 

169.2158 

193.2047 

220.5266 

251.6382 

59 

184.8683 

211.5591 

242.0280 

276.8020 

60 

201.9686 

231.6572 

265.6256 

304.4822 

61 

220.6507 

253.6647 

291.5241 

334.9304 

62 

241.0609 

277.7628 

319.9477 

368.4235 

63 

263.3590 

304.1502 

351.1426 

405.2659 

64 

287.7197 

333.0445 

385.3790 

445.7925 

65 

314.3338 

364.6838 

422.9534 

490.3718 

66 

343.4096 

399.3288 

464.1913 

539.4091 

67 

375.1750 

437.2650 

509.4498 

593.3500 

68 

409.8786 

478.8051 

559.1212 

652.6850 

69 

447.7923 

524.2915 

613.6355 

717.9535 

70 

489.2130 

574.0992 

673.4649 

789.7489 

71 

534.4652 

628.6386 

739.1277 

868.7238 

72 

583.9032 

688.3593 

811.1927 

955.5962 

73 

637.9142 

753.7534 

890.2840 

1051.156 

74 

696.9212 

825.3600 

977.0867 

1156.271 

75 

761.3862 

903.7692 

1072.352 

1271.898 


60 





TABLE I 


Rate, 9^?^ to 10% 
Years, 76 to 100 


COMPOUND INTEREST 

The value of $1 invested at a fixed rate of compound interest for one 
to one hundred years. 


Years 

91 / 4 % 

9%% 

9%% 

10% 

76 

831.8144 

989.6273 

1176.906 

1399.088 

77 

908.7572 

1083.642 

1291.655 

1538.996 

78 

992.8172 

1186.588 

1417.591 

1682.896 

79 

1084.652 

1299.314 

1555.806 

1862.186 

80 

1184.982 

1422.748 

1707.497 

2048.405 

81 

1294.593 

1557.909 

1873.978 

2253.246 

82 

1414.343 

1705.910 

2056.691 

2478.571 

83 

1545.169 

1867.972 

2257.218 

2726.428 

84 

1688.097 

2045.429 

2477.296 

2999.071 

85 

1844.246 

2239.744 

2718.832 

3298.978 

86 

2014.839 

2452.520 

2983.918 

3628.876 

87 

2201.211 

2685.509 

3274.850 

3991.763 

88 

2404.823 

2940.633 

3594.148 

4390.940 

89 

2627.269 

3219.993 

3944.577 

4830.034 

90 

2870.291 

3525.891 

4329.174 

5313.038 

91 

3135.793 

3860.851 

4751.268 

5844.342 

92 

3425.853 

4227.632 

5214.516 

6428.776 

93 

3742.744 

4629.257 

5722.931 

7071.654 

94 

4088.948 

5069.037 

6280.917 

7778.820 

95 

4467.175 

5550.595 

6893.305 

8556.702 

96 

4880.388 

6077.902 

7565.402 

9412.372 

97 

5331.824 

6655.302 

8303.019 

10353.61 

98 

5825.016 

7287.555 

9112.564 

11388.97 

99 

6363.830 

7979.872 

10001.05 

12527.87 

100 

6952.483 

8737.960 

10976.15 

13780.66 


61 






'V ' , ' 




V ;. 

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' ' ■ (',’< f ' ' 


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J\ n 


• J 


I -'X : -r. X v-. ■. 


y k 


*, •i.'H 


» A* »• 

* ^ jit t 

t'i. i 


*^r‘¥ 


t 




'\ 








TABLE II 

ANNUITY FOR INVESTMENT 


<7—1 


The value of $1 invested at the end of every year for one to one hundred 
y^rs at the following rates of compound interest. 


1% 

11/4% 

11/2% 

1%% 

2% 


2y2% 

2%% 

3% 

31/4% 

31/2% 

3%% 

4% 

41/4% 

41/4% 

4%% 

5% 

51/4% 

5%% 

5%% 

6% 

61/4% 

6%% 

6%% 

7% 

71/4% 

71/2% 

7%% 

8% 

81/4% 

81/2% 

8%% 

9% 

91/4% 

91/2% 

9%% 


First example—What amount will accumulate after 15 years, investing a 
capital of $1000 at the end of every year @5% per annum compound interest ? 
a=$1000 f/=1.05 n=15 

^ 1000(1.05"®—!) 1000(2.078928—1) 


1.05—1 


0.05 


=$21578.56 


<7"—1 1 05"®—1 

Table II, page 80, shows that or $1 invested at the end 

of every year for 15 years @5% per annum compound interest, becomes 
21.57856; therefore $1000 will become 

$1000 X21.57856=$21578.56 


Second example—What amount will accumulate after 15 years, investing a 
capital of $1000 at the beginning of every year @5% per annum compound 
interest ? 

Table II, page 80, shows that $1 invested at the end of every year, for 16 
years @ 5% per annum compound interest becomes $23.65748 

deduct one unit $ 1.00000 
$22.65748 

Therefore $1000 will become: 

$1000 X22.65748=$22,657.48 









Rate, 1% to 1%% 
Years, 1 to 25 


TABLE II 


ANNUITY FOR INVESTMENT 


The value of $1 invested at the end of every year at a fixed rate of 
compound interest for one to one hundred years. 


Years 

1% 

1%% 

1%% 


1 

1.000000 

1.000000 

1.000000 

1.000000 

2 

2.010000 

2.012480 

2.015000 

2.017486 

3 

3.030100 

3.037600 

3.045200 

3.052800 

4 

4.060400 

4.075600 

4.090866 

4.106229 

5 

5.101000 

5.126560 

5.152266 

5.178057 

6 

6.152000 

6.190640 

6.229466 

6.268686 

7 

7.213500 

7.268000 

7.322933 

7.378400 

8 

8.285700 

8.358880 

8.432733 

8.507543 

9 

9.368500 

9.463360 

9.559200 

9.656400 

10 

10.46220 

10.58160 

10.70260 

10.82537 

11 

11.56690 

11.71384 

11.86313 

12.01486 

12 

12.68250 

12.86024 

13.04106 

13.2268G 

13 

13.80940 

14.02104 

14.23673 

14.45651 

14 

14.94750 

15.19624 

15.45026 

15.70949 

15 

16.09700 

16.38624 

16.68200 

16.98440 

16 

17.25800 

17.59104 

17.93220 

18.28166 

17 

18.43050 

18.81096 

19.20120 

19.60154 

18 

19.61480 

20.04608 

20.48920 

20.94463 

19 

20.81100 

21.29664 

21.79653 

22.31109 

20 

22.01910 

22.56280 

23.12346 

23.70154 

21 

23.23930 

23.84488 

24.47033 

25.11629 

22 

24.47170 

25.14288 

25.83733 

26.55583 

23 

25.71640 

26.45720 

27.22486 

28.02057 

24 

26.97360 

27.78792 

28.63326 

29.51091 

25 

28.24330 

29.13528 

30.06273 

31.02737 


64 




TABLE II 


Rate. IX to mX 
Year9t 26 to 50 


ANNUITY FOR INVESTMENT 


The value of $1 invested at the end of every year at a fixed rate of 


compound interest for one to one hundred years. 

Years 

1% 

1%% 

lV2(fo 

m^o 

26 

29.52580 

30.49944 

31.51366 

32.59103 

27 

30.82100 

31.88064 

32.98640 

34.14029 

28 

32.12920 

33.27912 

34.48120 

35.73778 

29 

33.45050 

34.69512 

35.99840 

37.36320 

30 

34.78510 

36.12880 

37.53833 

39.01703 

31 

36.13290 

37.58040 

39.10146 

40.69983 

32 

37.49430 

39.05016 

40.68800 

42.41206 

33 

38.86920 

40.53824 

42.29826 

44.15429 

34 

40.25790 

42.04496 

43.93273 

45.92691 

35 

41.66050 

43.57056 

45.59166 

47.73069 

36 

43.07710 

45.11520 

47.27553 

49.56594 

37 

44.50790 

46.67912 

48.98466 

51.43337 

38 

45.95300 

48.26256 

50.71940 

53.33343 

39 

47.41250 

49.86584 

52.48020 

55.26680 

40 

48.88670 

51.48920 

54.26740 

57.23394 

41 

50.37550 

53.13280 

56.08146 

59.23554 

42 

51.87930 

54.79696 

57.92266 

61.27217 

43 

53.39810 

56.48192 

59.79146 

63.34440 

44 

54.93210 

58.18792 

61.68833 

65.45291 

45 

56.48150 

59.91520 

63.61360 

67.59834 

46 

58.04630 

61.66416 

65.56780 

69.78131 

47 

59.62670 

63.43496 

67.55126 

72.00251 

48 

61.22300 

65.22784 

69.56453 

74.26251 

49. 

62.83520 

67.04320 

71.60800 

76.56211 

50 

64.46360 

68.88128 

73.68206 

78.90194 


10 


65 




Rate, 1% to l%% 
Years, . 51 to 75 


TABLE II 


ANNUITY FOR INVESTMENT 

The value of $1 invested at the end of every year at a fixed rate of 
compound interest for one to one hundred years. 


Years 

1% 

1%% 

1%% 

1%% 

51 

66.10830 

70.74224 

75.78733 

81.28269 

52 

67.76940 

72.62656 

77.92413 

83.70520 

53 

69.44700 

74.53432 

80.09300 

86.17000 

54 

71.14150 

76.46600 

82.29433 

88.67794 

55 

72.85300 

78.42184 

84.52873 

91.22983 

56 

74.58150 

80.40216 

86.79667 

93.82634 

57 

76.32740 

82.40712 

89.09860 

96.46829 

58 

78.09060 

84.43720 

91.43507 

99.15646 

59 

79.87150 

86.49264 

93.80660 

101.8917 

60 

81.67030 

88.57376 

96.21367 

104.6748 

61 

83.48700 

90.68096 

98.65687 

107.5066 

62 

85.32190 

92.81440 

101.1367 

110.3880 

63 

87.17510 

94.97464 

103.6537 

113.3198 

64 

89.04680 

97.16176 

106.2085 

116.3029 

65 

90.93730 

99.37632 

108.8016 

119.3382 

66 

92.84670 

101.6185 

111.4336 

122.4265 

67 

94.77520 

103.8886 

114.1051 

125.5690 

68 

96.72290 

106.1873 

116.8167 

128.7665 

69 

98.69020 

108.5146 

119.5689 

132.0199 

70 

100.6771 

110.8710 

122.3625 

135.3302 

71 

102.6839 

113.2569 

125.1980 

138.6985 

72 

104.7108 

115.6726 

128.0759 

142.1257 

73 

106.7579 

118.1185 

130.9970 

145.6129 

74 

108.8254 

120.5950 

133.9620 

149.1611 

75 

110.9137 

123.1023 

136.9713 

152.7714 


66 





TABLE II 


Rate, 1% to \%% 
Years, 76 to 100 


ANNUITY FOR INVESTMENT 


The value of $1 invested at the end of every year at a fixed rate of 


compound interest for one to one hundred years. 

Years 

1% 


1%% 


76 

113.0229 

125.6411 

140.0258 

156.4449 

77 

115.1532 

128.2116 

143.1262 

160.1826 

78 

117.3047 

130.8142 

146.2731 

163.9859 

79 

119.4777 

133.4494 

149.4671 

167.8556 

80 

121.6726 

136.1175 

152.7091 

171.7930 

81 

123.8893 

138.8190 

155.9997 

175.7995 

82 

126.1282 

141.5542 

159.3397 

179.8759 

83 

128.3895 

144.3236 

162.7298 

184.0238 

84 

130.6734 

147.1276 

166.1707 

188.2441 

85 

132.9802 

149.9667 

169.6633 

192.5384 

86 

135.3100 

152.8413 

173.2082 

196.9078 

87 

137.6631 

155.7518 

176.8063 

201.3537 

88 

140.0397 

158.6986 

180.4584 

205.8774 

89 

142.4401 

161.6824 

184.1653 

210.4802 

90 

144.8646 

164.7034 

187.9276 

215.1636 

91 

147.3132 

167.7622 

191.7465 

219.9290 

92 

149.7864 

170.8591 

195.6227 

224.7777 

93 

152.2842 

173.9949 

199.5571 

229.7113 

94 

154.8071 

177.1698 

203.5504 

234.7312 

95 

157.3552 

180.3844 

207.6035 

239.8391 

96 

159.9287 

183.6392 

211.7176 

245.0361 

97 

162.5280 

186.9346 

215.8933 

250.3243 

98 

165.1533 

190.2714 

220.1317 

255.7049 

99 

167.8049 

193.6498 

224.4336 

261.1798 

100 

170.4830 

197.0703 

228.8001 

266.7505 


67 





Rate, 2% to 23/4% 
Year*, 1 to 25 


TABLE II 

ANNUITY FOR INVESTMENT 


The value of $1 invested at the end of every year at a fixed rate of 
compound interest for one to one hundred years. 


Years 

2% 

2%% 

2%% 

2%% 

1 

1.000000 

1.000000 

1.000000 

1.000000 

2 

2.020000 

2.022489 

2.025000 

2.027491 

3 

3.060400 

3.067956 

3.075600 

3.083236 

4 

4.121600 

4.136978 

4.152520 

4.168036 

5 

5.204000 

5.230089 

5.256320 

5.282655 

6 

6.308100 

6.347778 

6.387720 

6.427927 

7 

7.434200 

7.490622 

7.547440 

7.604691 

8 

8.583000 

8.659111 

8.736120 

8.813818 

9 

9.754650 

9.854000 

9.954520 

10.05618 

10 

10.94975 

11.07569 

11.20340 

11.33273 

11 

12.16875 

12.32489 

12.48348 

12.64436 

12 

13.41210 

13.60218 

13.79560 

13.99211 

13 

14.68035 

14.90822 

15.14048 

15.37687 

14 

15.97400 

16.24364 

16.51900 

16.79975 

15 

17.29345 

17.60915 

17.93200 

18.26175 

16 

18.63930 

19.00533 

19.38028 

19.76393 

17 

20.01210 

20.43293 

20.86480 

21.30745 

18 

21.41235 

21.89267 

22.38640 

22.89338 

19 

22.84060 

23.38524 

23.94608 

24.52295 

20 

24.29745 

24.91147 

25.54476 

26.19731 

21 

25.78340 

26.47196 

27.18336 

27.91775 

22 

27.29905 

28.06756 

28.86296 

29.68549 

23 

28.84505 

29.69907 

30.58452 

31.50182 

24 

30.42195 

31.36729 

32.34916 

33.36811 

25 

32.03040 

33.07307 

34.15788 

35.28571 


68 





TABLE II 


Rate, 2% to 2%% 
Years, 26 to 50 


ANNUITY FOR INVESTMENT 


The value of $1 invested at the end of every year at a fixed rate of ^ 


compound interest for one to one hundred years. 

Years 

2% 

2%% 

21/2% 

2%% 

26 

33.67100 

34.81720 

36.01184 

37.25607 

27 

35.34445 

36.60058 

37.91212 

39.28058 

28 

37.05135 

38.42409 

39.85992 

41.36080 

29 

38.79235 

40.28862 

41.85644 

43.49822 

30 

40.56815 

42.19516 

43.90288 

45.69444 

31 

42.37955 

44.14453 

46.00048 

47.95102 

32 

44.22715 

46.13778 

48.15048 

50.26967 

33 

46.11165 

48.17587 

50.35424 

52.65207 

34 

48.03390 

50.25982 

52.61312 

55.10000 

35 

49.99470 

52.39067 

54.92848 

57.61524 

36 

51.99460 

54.56942 

57.30172 

60.19967 

37 

54.03450 

56.79716 

59.73424 

62.85516 

38 

56.11520 

59.07511 

62.22760 

65.58367 

39 

58.23750 

61.40431 

64.78328 

68.38720 

40 

60.40225 

63.78604 

67.40288 

71.26782 

41 

62.61030 

66.22120 

70.08796 

74.22767 

42 

64.86250 

68.71107 

72.84016 

77.26895 

43 

67.15975 

71.25716 

75.66116 

80.39382 

44 

69.50300 

73.86040 

78.55272 

83.60465 

45 

71.89305 

76.52227 

81.51656 

86.90378 

46 

74.33090 

79.24400 

84.55448 

90.29364 

47 

76.81755 

82.02698 

87.66832 

93.77669 

48 

79.35390 

84.87258 

90.86004 

97.35556 

49 

81.94100 

87.78218 

94.13156 

101.0328 

50 

84.57980 

90.75738 

97.48488 

104.8112 


69 





Rate, 2% to 2%% 
Years, 51 to 75 


TABLE II 


ANNUITY FOR INVESTMENT 


The value of $1 invested at the end of every year at a fixed rate of 
componnd interest for one to one hundred years. 


Years 

2% 

2%% 

2%% 

2%% 

51 

87.27140 

93.79942 

100.9220 

108.6935 

52 

90.01685 

96.90991 

104.4451 

112.6826 

53 

92.81720 

100.0904 

108.0562 

116.7813 

54 

95.67355 

103.3424 

111.7576 

120.9928 

55 

98.58705 

106.6676 

115.5516 

125.3201 

56 

101.5588 

110.0676 

119.4404 

129.7664 

57 

104.5900 

113.5441 

123.4264 

134.3349 

58 

107.6818 

117.0988 

127.5121 

139.0291 

59 

110.8354 

120.7336 

131.6999 

143.8524 

60 

114.0522 

124.4500 

135.9924 

148.8083 

61 

117.3332 

128.2502 

140.3922 

153.9006 

62 

120.6798 

132.1358 

144.9021 

159.1328 

63 

124.0935 

136.1088 

149.5246 

164.5089 

64 

127.5754 

140.1713 

154.2628 

170.0329 

65 

131.1269 

144.3252 

159.1193 

175.7088 

66 

134.7494 

148.5725 

164.0973 

181.5408 

67 

138.4444 

152.9153 

169.1998 

187.5332 

68 

142.2133 

157.3559 

174.4298 

193.6903 

69 

146.0576 

161.8964 

179.7906 

200.0168 

70 

149.9788 

166.5391 

185.2854 

206.5173 

71 

153.9784 

171.2862 

190.9175 

213.1965 

72 

158.0580 

176.1401 

196.6905 

220.0593 

73 

162.2192 

181.1032 

202.6078 

227.1109 

74 

166.4636 

186.1780 

208.6730 

234.3565 

75 

170.7928 

191.3671 

214.8898 

241.8012 


70 




TABLE II 


Rate, 2% to 
Years, 76 to 100 


ANNUITY FOR INVESTMENT 

The value of $1 invested at the end of everj^ year at a fixed rate of 
compound interest for one to one hundred years. 


Years 

2% 

2%% 

21/2% 

2%% 

76 

175.2087 

196.6728 

221.2621 

249.4507 

77 

179.7129 

202.0980 

227.7936 

257.3106 

78 

184.3072 

207.6452 

234.4885 

265.3867 

79 

188.9933 

213.3172 

241.3507 

273.6848 

80 

193.7732 

219.1168 

248.3845 

282.2111 

81 

198.6487 

225.0469 

255.5942 

290.9719 

82 

203.6217 

231.1104 

262.9840 

299.9736 

83 

208.6941 

237.3104 

270.5587 

309.2228 

84 

213.8680 

243.6499 

278.3226 

318.7265 

85 

219.1454 

250.1320 

286.2808 

328.4913 

86 

224.5283 

256.7600 

294.4378 

338.5247 

87 

230.0189 

263.5371 

302.7988 

348.8342 

88 

235.6193 

270.4666 

311.3688 

359.4273 

89 

241.3317 

277.5521 

320.1531 

370.3113 

90 

247.1584 

284.7970 

329.1570 

381.4949 

91 

253.1016 

292.2049 

338.3859 

392.9858 

92 

259.1636 

299.7795 

347.8465 

404.7931 

93 

265.3469 

307.5245 

357.5417 

416.9247 

94 

271.6539 

315.4439 

367.4804 

429.3898 

95 

278.0870 

323.5413 

377.6672 

442.1985 

96 

284.6487 

331.8210 

388.1088 

455.3589 

97 

291.3417 

340.2869 

398.8116 

468.8813 

98 

298.1685 

348.9434 

409.7820 

482.7756 

99 

305.1320 

357.7946 

421.0268 

497.0520 

100 

312.2347 

366.8449 

432.5524 

511.7207 


71 




Rale. 3X to 3%% 
Years. 1 to 25 


TABLE 11 


ANNUITY FOR INVESTMENT 


The value of $1 invested at the end of every year at a fixed rate of 
compound interest for one to one hundred years. 


Years 


31 / 4 % 

31 / 2^0 

3%% 

1 

1.000000 

1.000000 

1.000000 

1.000000 

2 

2.030000 

2.032492 

2.035000 

2.037493 

3 

3.090900 

3.098554 

3.106200 

3.113920 

4 

4.183633 

4.199262 

4.214914 

4.230693 

5 

5.309133 

5.335754 

5.362428 

5.389333 

6 

6.468366 

6.509169 

6.550114 

6.591440 

7 

7.662433 

7.720707 

7.779371 

7.838615 

8 

8.892300 

9.971631 

9.051628 

9.132560 

9 

10.15906 

10.26320 

10.36845 

10.47504 

10 

11.46383 

11.59677 

11.73134 

11.86787 

11 

12.80776 

12.97366 

13.14191 

13.31288 

12 

14.19200 

14.39532 

14.60188 

14.81213 

13 

15.61773 

15.86317 

16.11294 

16.36760 

14 

17.08626 

17.37874 

17.67688 

17.98139 

15 

18.59886 

19.94357 

19.29557 

19.65565 

16 

20.15683 

20.55923 

20.97091 

21.39275 

17 

21.76153 

22.22742 

22.70491 

23.19499 

18 

23.41436 

23.94978 

24.49957 

25.06480 

19 

25.11680 

25.72815 

26.35708 

27.00472 

20 

26.87030 

27.56434 

28.27954 

29.01736 

21 

28.67640 

29.46018 

30.26931 

31.10552 

22 

30.53670 

31.41763 

32.32874 

33.27198 

23 

32.45280 

33.43871 

34.46026 

35.51971 

24 

34.42636 

35.52548 

36.66634 

37.85165 

25 

36.45913 

37.68009 

72 

38.94966 

40.27109 




TABLE II 


Rate, 3%to3%% 
Years, 26 to 50 


ANNUITY FOR INVESTMENT 


The value of $1 invested at the end of every year at a fixed rate of 
compound interest for one to one hundred years. 


Years 

3% 

31 / 4^0 

31 / 2 % 

3%% 

26 

38.55290 

39.90471 

41.31291 

42.78125 

27 

40.70950 

42.20161 

43.75886 

54.38555 

28 

42.93080 

44.57317 

46.29037 

48.08752 

29 

45.21870 

47.02179 

48.91051 

50.89080 

30 

47.57523 

49.55000 

51.62240 

53.79920 

31 

50.00250 

52.16037 

54.42920 

56.81667 

32 

52.50257 

54.85560 

57.33420 

59.94731 

33 

55.07763 

57.63840 

60.34086 

63.19533 

34 

57.72997 

60.51166 

63.45280 

66.56515 

35 

60.46187 

63.47834 

66.67363 

70.06133 

36 

63.27573 

66.54139 

70.00720 

73.68864 

37 

66.17400 

69.70400 

73.45743 

77.45197 

38 

69.15923 

72.96939 

77.02845 

81.35640 

39 

72.23400 

76.34089 

80.72443 

85.40728 

40 

75.40100 

79.82200 

84.54977 

89.61005 

41 

78.66303 

83.41622 

88.50900 

93.97043 

42 

82.02290 

87.12726 

92.60680 

98.49432 

43 

85.48360 

90.95890 

96.84806 

103.1879 

44 

89.04810 

94.91508 

101.2377 

108.0574 

45 

92.71953 

98.99982 

105.7809 

113.1095 

46 

96.50113 

103.2173 

110.4833 

118.3511 

47 

100.3961 

107.5718 

115.3502 

123.7893 

48 

104.4080 

112.0679 

120.3874 

129.4314 

49 

108.5402 

116.7102 

125.6010 

135.2851 

50 

112.7964 

121.5033 

130.9970 

141.3582 


73 




Rate, Z% to 3%% 
Years, 51 to 75 


TABLE II 


ANNOITY FOR INVESTMENT 


The value of $1 invested at the end of every year at a fixed rate of 
compound interest for one to one hundred years. 


Years 

3% 

3%% 

31 / 2 % 

3%% 

51 

117.1804 

126.4522 

136.5819 

147.6592 

52 

121.6958 

131.5619 

142.3622 

154.1964 

53 

126.3466 

136.8377 

148.3449 

160.9787 

54 

131.1370 

142.2849 

154.5369 

168.0155 

55 

136.0711 

147.9092 

160.9457 

175.3161 

56 

141.1532 

153.7162 

167.5787 

182.8904 

57 

146.3878 

159.7120 

174.4440 

190.7488 

58 

151.7794 

165.9027 

181.5495 

198.9019 

59 

157.3328 

172.2945 

188.9037 

207.3607 

60 

163.0527 

178.8942 

196.5153 

216.1367 

61 

168.9443 

185.7083 

204.3933 

225.2418 

62 

175.0132 

192.7438 

212.5471 

234.6884 

63 

181.2630 

200.0080 

220.9862 

244.4893 

64 

187.7009 

207.5083 

229.7207 

254.6576 

65 

194.3319 

215.2523 

238.7609 

265.2072 

66 

201.1618 

223.2480 

248.1175 

276.1525 

67 

208.1967 

231.5036 

257.8017 

287.5083 

68 

215.4426 

240.0274 

267.8249 

299.2896 

69 

222.9058 

248.8283 

278.1983 

311.5131 

70 

230.5930 

257.9154 

288.9351 

324.1949 

71 

238.5108 

267.2976 

300.0480 

337.3523 

72 

246.6661 

276.9849 

311.5497 

351.0029 

73 

255.0661 

286.9868 

323.4537 

365.1656 

74 

263.7181 

297.3138 

335.7746 

379.8592 

75 

272.6296 

307.9766 

348.5266 

395.1037 


74 




TABLE 11 


Rate, 3% to 3%% 
Years, 76 to 100 


ANNUITY FOR INVESTMENT 


The value of $1 invested at the end of every year at a fixed rate of 


compound interest for one to one hundred years. 

Years 

3% 

3%% 

3T2% 

3%% 

76 

281.8085 

318.9858 

361.7251 

410.9203 

77 

291.2627 

330.3529 

375.3855 

427.3296 

78 

301.0007 

342.0895 

389.5240 

444.3544 

79 

311.0307 

354.2074 

404.1571 

462.0179 

80 

321.3613 

366.7194 

419.3026 

480.3437 

81 

332.0023 

379.6378 

434.9780 

499.3565 

82 

342.9623 

392.9760 

451.2023 

519.0824 

83 

354.2513 

406.7477 

467.9943 

539.5469 

84 

365.8787 

420.9671 

485.3740 

560.7811 

85 

377.8550 

435.6486 

503.3620 

582.8101 

86 

390.1907 

450.8074 

521.9797 

605.6656 

87 

402.8963 

466.4588 

541.2491 

629.3779 

88 

415.9833 

482.6188 

561.1929 

653.9795 

89 

429.4627 

499.3040 

581.8346 

679.5037 

90 

443.3463 

516.5311 

603.1986 

705.9853 

91 

457.6467 

534.3185 

625.3105 

733.4597 

92 

472.3760 

552.6837 

648.1963 

761.9645 

93 

487.5473 

571.6462 

671.8831 

791.5381 

94 

503.1737 

591.2246 

696.3988 

822.2208 

95 

519.2690 

611.4394 

721.7726 

854.0541 

96 

535.8470 

632.3115 

748.0346 

887.0811 

97 

552.9223 

653.8615 

775.2157 

921.3467 

98 

570.5100 

676.1120 

803.3483 

956.8971 

99 

588.6253 

699.0855 

832.4654 

993.7808 

100 

607.2840 

722.8058 

862.6014 

1032.047 





Rate, 4% to 4%% 
Years, 1 to 25 


TABLE II 


ANNUITY FOR INVESTMENT 

The value of $1 invested at the end of every year at a fixed rate of 
compound interest for one to one hundred years. 


Years 

4% 

41 / 4 % 


4%fo 

1 

1.000000 

1.000000 

1.000000 

1.000000 

2 

2.040000 

2.042494 

2.045000 

2.047495 

3 

3.121600 

3.129294 

3.137022 

3.144758 

4 

4.246450 

4.262306 

4.278177 

4.294126 

5 

5.416300 

5.443439 

5.470688 

5.497179 

6 

6.632950 

6.674800 

6.716889 

6.759263 

7 

7.898250 

7.958494 

8.019155 

8.080316 

8 

9.214200 

9.296729 

9.380022 

9.464126 

9 

10.58275 

10.69184 

10.80211 

10.91368 

10 

12.00607 

12.14626 

12.28820 

12.43206 

11 

13.48630 

13.66247 

13.84117 

14.02259 

12 

13.02575 

15.24313 

15.46402 

15.68865 

13 

16.62677 

16.89096 

17.15991 

17.43387 

14 

18.29185 

18.60882 

18.93211 

19.26198 

13 

20.02352 

20.39972 

20.78406 

21.17690 

16 

21.82445 

22.26671 

22.71933 

23.18280 

17 

23.69742 

24.21304 

24.74171 

25.28400 

18 

25.64532 

26.24209 

26.85509 

27.48497 

19 

27.67115 

28.35739 

29.06355 

29.79053 

20 

29.77797 

30.56260 

31.37144 

32.20556 

21 

31.96910 

32.86131 

33.78315 

34.73530 

22 

34.24785 

33.25812 

36.30340 

37.38524 

23 

36.61777 

37.75659 

38.93704 

40.16105 

24 

39.08247 

40.36125 

41.68922 

43.06867 

25 

41.64575 

43.07664 

44.56524 

46.11444 


76 




TABLE 11 

ANNUITY FOR INVESTMENT 


Rate, 4% to 
Years, 26 to 50 


The value of $1 invested at the end of every year at a fixed rate of 
oompound interest for one to one hundred years. 


Years 

4% 


4^4% 

4%% 

26 

44.31157 

45.90739 

47.57069 

49.30488 

27 

47.08405 

48.85845 

50.71135 

52.64684 

28 

49.96740 

51.93494 

53.99338 

56.14756 

29 

52.96610 

55.14219 

57.42307 

59.81457 

30 

56.08470 

58.48574 

61.00709 

63.65575 

31 

59.32810 

61.97139 

64.75242 

67.67939 

32 

62.70120 

65.60518 

68.66627 

71.89415 

33 

66.20925 

69.39339 

72.75627 

76.30912 

34 

69.85760 

73.34261 

77.03031 

80.93379 

35 

73.65190 

77.45972 

81.49669 

85.77813 

36 

77.59797 

81.75174 

86.16404 

90.85263 

37 

81.70187 

86.22619 

91.04142 

96.16811 

38 

85.96997 

90.89080 

96.13829 

101.7361 

39 

90.40875 

95.75367 

101.4645 

107.5685 

40 

95.02507 

100.8232 

107.0304 

113.6780 

41 

99.82607 

106.1082 

112.8468 

120.0777 

42 

104.8191 

111.6178 

118.9249 

126.7814 

43 

110.0118 

117.3616 

125.2765 

133.8035 

44 

115.4123 

123.3495 

131.9140 

141.1592 

45 

121.0288 

129.5919 

138.8501 

148.8642 

46. 

126.8699 

136.0995 

146.0983 

156.9352 

47 

132.9447 

142.8838 

153.6728 

165.3896 

48 

139.2624 

149.9563 

161.5881 

174.2457 

49 

145.8329 

157.3295 

169.8595 

183.5223 

50 

152.6663 

165.0161 

77 

178.5032 

193.2396 





Rate, A% to 4%% 
Years, 51 to 75 


TABLE II 


ANNUITY FOR INVESTMENT 


The value of $1 invested at the end of every year at a fixed rate of 


compound interest for one to one hundred years. 

Years 

4% 

41 / 4 % 


4%^o 

51 

159.7729 

173.0292 

187.5359 

203.4185 

52 

167.1638 

181.3830 

196.9750 

214.0808 

53 

174.8504 

190.0918 

206.8389 

225.2497 

54 

182.8444 

199.1707 

217.1467 

236.9491 

55 

191.1582 

208.6355 

227.9182 

249.2040 

56 

199.8045 

218.5026 

239.1744 

262.0413 

57 

208.7966 

228.7889 

250.9373 

275.4880 

58 

218.1485 

239.5125 

263.2296 

289.5737 

59 

227.8743 

250.6918 

276.0749 

304.3284 

60 

237.9893 

262.3461 

289.4982 

319.7842 

61 

248.5088 

274.4958 

303.5258 

335.9739 

62 

259.4490 

287.1619 

318.1844 

352.9326 

63 

270.8270 

300.3664 

333.5027 

370,6968 

64 

282.6600 

314.1320 

349.5102 

389.3048 

65 

294.9665 

328.4826 

366.2382 

408.7968 

66 

307.7650 

343.4431 

383.7189 

429.2145 

67 

321.0755 

359.0395 

401.9862 

450.6025 

68 

334.9185 

375.2988 

421.0758 

473.0059 

69 

349.3153 

392.2489 

441.0242 

496.4737 

70 

364.2878 

409.9198 

461.8704 

521.0563 

71 

379.8593 

428.3414 

483.6547 

546.8061 

72 

396.0535 

447.5459 

506.4191 

573.7796 

73 

412.8958 

407.5666 

530.2080 

602.0339 

74 

430.4115 

488.4381 

555.0673 

631.6305 

75 

448.6280 

510.1969 

581.0453 

662.6328 


78 




TABLE II 

ANNUITY FOR INVESTMENT 


Rate. 4 % to 43/4%- 
Years, 76 to 100 


The value of $1 invested at the end of every year at a fixed rate of 
compound interest for one to one hundred years. 


Years 

4% 

4V4% . 


4%% 

76 

467.5730 

532.8802 

608.1924 

695.1078 

77 

487.2760 

556.5278 

636.5611 

729.1255 

78 

507.7670 

581.1802 

666.2065 

764.7587 

79 

529.0778 

606.8802 

697.1856 

802.0853 

80 

551.2408 

633.6727 

729.5589 

841.1840 

81 

574.2905 

661.6038 

763.3891 

882.1400 

82 

598.2620 

690.7219 

798.7416 

925.0415 

83 

623.1925 

721.0776 

835.6851 

969.9812 

84 

649.1200 

752.7235 

874.2909 

1017.055 

85 

676.0848 

785.7146 

914.6340 

1066.365 

86 

704.1280 

820.1075 

956.7927 

1118.017 

87 

733.2930 

855.9621 

1000.848 

1172.123 

88 

763.6250 

893.3405 

1046.886 

1228.799 

89 

795.1698 

932.3075 

1094.996 

1288.167 

90 

827.9763 

972.9311 

1145.271 

1350.354 

91 

862.0952 

1015.280 

1197.809 

1415.496 

92 

897.5788 

1059.430 

1252.710 

1483.732 

93 

934.4820 

1105.456 

1310.082 

1555.209 

94 

972.8612 

1153.438 

1370.036 

1630.081 

95 

1012.775 

1203.459 

1432.687 

1708.510 

96 

1054.286 

1255.606 

1498.158 

1790.664 

97 

1097.458 

1309.970 

1566.575 

1876.721 

98 

1142.356 

1366.644 

1638.071 

1966.865 

99 

1189.050 

1425.726 

1712.785 

2061.291 

100 

1237.612 

1487.320 

1790.860 

2160.202 


79 





Rate, 5XtoS%X 
Years, 1 to 25 


TABLE II 


ANNUITY FOR INVESTMENT 


The value of $1 invested at the end of eveay year at a fixed rate of 
compound interest for one to one hundred years. 


Years 

5% 

5%% 

5%% 

5%% 

1 

1.000000 

1.000000 

1.000000 

1.000000 

2 

2.050000 

2.052495 

2.055000 

2.057496 

3 

3.152500 

3.160248 

3.168018 

3.175809 

4 

4.310120 

4.326171 

4.342254 

4.358417 

5 

5.525620 

5.553295 

5.581091 

5.609026 

6 

6.801900 

6.844838 

6.888054 

6.931548 

7 

8.142000 

8.204190 

8.266909 

8.330122 

8 

9.549100 

9.634915 

9.721582 

9.809096 

9 

11.02656 

11.14074 

11.25627 

11.37315 

10 

12.57788 

12.72564 

12.87536 

13.02708 

11 

14.20678 

14.39373 

14.58353 

14.77614 

12 

15.91712 

16.14941 

16.38562 

16.62577 

13 

17.71298 

17.99726 

18.28683 

18.58176 

14 

19.59862 

19.94211 

20.29260 

20.65024 

15 

21.57856 

21.98907 

22.40871 

22.83760 

16 

23.65748 

24.14349 

24.64120 

25.15092 

17 

25.84036 

26.41103 

26.99647 

27.59710 

18 

28.13238 

28.79760 

29.48127 

30.18376 

19 

• 30.53900 

31.30949 

32.10274 

32.91932 

20 

33.06594 

33.95322 

34.86842 

35.81219 

21 

35.71924 

36.73577 

37.78618 

38.87139 

22 

38.50520 

39.66440 

40.86442 

42.10650 

23 

41.43046 

42.74678 

44.11196 

45.52762 

24 

44.50198 

45.99097 

47.53812 

49.14546 

25 

47.72708 

49.40549 

51.15272 

52.97134 


80 





TABLE II 


Rate, 55^ to 5%%': 
Years, 26 to 50 


ANNUITY FOR INVESTMENT 


The value of $1 invested at the end of every year at a fixed rate of 
compound interest for one to one hundred years. 

Years 

5% 

5%% 

51 / 2^0 

5%^o 

26 

51.11344 

52.99928 

54.96613 

57.01720 

27 

54.66912 

56.78173 

58.98927 

61.29569 

28 

58.40258 

60.76278 

63.23369 

65.82019 

29 

62.32270 

64.95282 

67.71156 

70.60485 

30 

66.43886 

69.36286 

72.43573 

75.66464 

31 

70.76080 

74.00440 

77.41969 

81.01537 

32 

75.29884 

78.88964 

82.67778 

86.67376 

33 

80.06378 

84.03133 

88.22503 

92.65751 

34 

85.06698 

89.44297 

94.07747 

98.98530 

35 

90.32030 

95.13870 

100.2517 

105.6770 

36 

95.83632 

101.1335 

106.7656 

112.7536 

37 

101.6281 

107.4430 

113.6377 

120.2367 

38 

107.7095 

114.0838 

120.8878 

128.1504 

39 

114.0950 

121.0732 

128.5367 

136.5190 

40 

120.7997 

128.4295 

136.6062 

145.3689 

41 

127.8397 

136.1721 

145.1195 

154.7276 

42 

135.2317 

144.3211 

154.1011 

164.6245 

43 

142.9933 

152.8979 

163.5767 

175.0903 

44 

151.1430 

161.9251 

173.5734 

186.1581 

45 

159.7001 

171.4261 

184.1200 

197.8621 

46 

168.6852 

181.4261 

195.2467 

210.2393 

47 

178.1194 

191.9509 

206.9853 

223.3280 

48 

188.0254 

203.0282 

219.3694 

237.1694 

49 

198.4266 

214.6872 

232.4349 

251.8066 

50 

209.3480 

226.9583 

246.2187 

267.2856 


n 

81 






Rate, S%ioS%% 
Years, 51 to 75 


TABLE II 


ANNUITY FOR INVESTMENT 


The value of $1 invested at the end of every year at a fixed rate of 
compound interest for one to one hundred years. 


Years 

5^/o 


51 / 2-56 

5%% 

51 

220.8154 

239.8735 

260.7607 

283.6544 

52 

232.8562 

253.4669 

276.1027 

300.9647 

53 

245.4990 

267.7739 

292.2884 

319.2701 

54 

258.7738 

282.8322 

309.3644 

338.6282 

55 

272.7126 

298.6810 

327.3793 

359.0995 

56 

287.3482 

315.3617 

346.3851 

380.7475 

57 

302.7156 

332.9181 

366.4364 

403.6405 

58 

318.8518 

351.3964 

387.5904 

427.8499 

59 

335.7940 

370.8446 

409.9078 

453.4513 

60 

353.5838 

391.3139 

433.4527 

480.5249 

61 

372.2630 

412.8579 

458.2927 

509.1550 

62 

391.8778 

435.5330 

484.4990 

539.4315 

63 

412.4700 

459.3983 

512.1464 

571.4489 

64 

434.0934 

484.5168 

541.3145 

605.3071 

65 

456.7980 

510.9539 

572.0869 

641.1122 

66 

480.6380 

538.7790 

604.5518 

678.9763 

67 

505.6698 

568.0650 

638.8022 

719.0174 

68 

531.9532 

598.8884 

674.9362 

761.3610 

69 

559.5508 

631.3299 

713.0580 

806.1393 

70 

588.5284 

665.4749 

753.2762 

853.4923 

71 

618.9548 

701.4124 

795.7065 

903.5681 

72 

650.9026 

739.2366 

840.4705 

956.5235 

73 

684.4476 

779.0465 

887.6964 

1012.524 

74 

719.6700 

820.9463 

937.5198 

1071.744 

75 

756.6538 

865.0457 

990.0834 

1134.369 


82 




TABLE II 


Rate, S%toS%% 
Years, 76 to 100 


ANNUITY FOR INVESTMENT 


The value of $1 invested at the end of every year at a fixed rate of 


compound interest for one to one hundred years. 

Years 

5% 

5Vi</o 

5%% 

5%fo 

76 

795.4864 

911.4606 

1045.538 

1200.596 

77 

836.2608 

960.3124 

1104.043 

1270.630 

78 

879.0738 

1011.729 

1165.765 

1344.691 

79 

924.0276 

1065.845 

1230.883 

1423.011 

80 

971.2288 

1122.801 

1299.581 

1505.834 

81 

1020.790 

1182.748 

1372.058 

1593.419 

82 

1072.830 

1245.843 

1448.521 

1686.041 

83 

1127.471 

1312.250 

1529.190 

1783.988 

84 

1184.845 

1382.142 

1614.296 

1887.569 

85 

1245.087 

1455.705 

1704.083 

1997.103 

86 

1308.341 

1533.130 

1798.807 

2112.937 

87 

1374.758 

1614.619 

1898.742 

2235.431 

88 

1444.496 

1700.386 

2004.173 

2364.969 

89 

1517.721 

1790.657 

2115.402 

2501.955 

90 

1594.607 

1885.666 

2232.749 

2646.817 

91 

1675.338 

1985.663 

2356.551 

2800.009 

92 

1760.105 

2090.910 

2487.160 

2962.009 

93 

1849.110 

2201.684 

2624.955 

3133.325 

94 

1942.565 

2318.272 

2770.327 

3314.493 

95 

2040.694 

2440.981 

2923.696 

3506.075 

96 

2143.728 

2570.133 

3085.500 

3708.675 

97 

2251.914 

2706.065 

3256.203 

3922.923 

98 

2365.510 

2849.133 

3436.295 

4149.492 

99 

. 2484.786 

2999.714 

3626.289 

4389.089 

100 

2610.024 

3158.196 

3826.736 

4642.461 


83 




Rate, 6% to 6%% 
Years, 1 to 25 


TABLE n 

ANNUITY FOR INVESTMENT 


Tflie value of $1 invested at the end of every year at a fixed rate of 
compound interest for one to one hundred years. 


Years 6% 


1 

1.000000 

1.000000 

1.000000 

1.000000 

2 

2.060000 

2.062496 

2.065000 

2.067496 

3 

3.183600 

3.191408 

3.199215 

3.207052 

4 

4.374600 

4.390864 

4.407169 

4.423526 

5 

5.637083 

5.665296 

5.693630 

5.722119 

6 

6.975330 

7.019376 

7.063723 

7.108356 

7 

8.393850 

8.458096 

8.522861 

8.588178 

8 

9.897483 

9.986720 

10.07684 

10.16788 

9 

11.49133 

11.61088 

11.73184 

11.85422 

10 

13.18082 

13.33654 

13.49440 

13.65439 

11 

14.97166 

15.17008 

15.37153 

15.57604 

12 

16.86996 

17.11821 

17.37069 

17.62743 

13 

18.88216 

19.18810 

19.49978 

19.81729 

14 

21.01510 

21.38734 

21.76727 

22.15496 

15 

23.27601 

23.72405 

24.18215 

24.65043 

16 

25.67258 

26.20680 

26.75400 

27.31433 

17 

28.21294 

28.84472 

29.49301 

30.15804 

18 

30.90571 

31.64752 

32.41006 

33.19372 

19 

33.76006 

34.62549 

35.51671 

36.43428 

20 

36.78566 

37.78954 

38.82529 

39.89362 

21 

39.99280 

41.15139 

42.34894 

43.58643 

22 

43.39238 

44.72336 

46.10161 

47.52852 

23 

46.99591 

48.51856 

50.09821 

51.73670 

24 

50.81568 

52.55096 

54.35458 

56.22893 

25 

54.86465 

56.83539 

58.88763 

61.02439 


84 





R»le, 6% to mX 
• Years, 26 to 50 


TABLE II 

ANNUITY FOR INVESTMENT 


The value of $1 invested at the end of every year at a fixed rate of 
compound interest for one to ope hundred years. 


Years 

6 % 

GVi^o 

6V2^0 

6 %% 

26 

59.15653 

61.38760 

63.71532 

66.14353 

27 

63.70593 

66.22432 

68.85684 

71.60821 

28 

68.52830 

71.36333 

74.33254 

77.44178 

29 

73.64001 

76.82354 

80.16414 

83.66911 

30 

79.05841 

82.62498 

86.37478 

90.31677 

31 

84.80192 

88.78904 

92.98915 

97.41314 

32 

90.89003 

95.33835 

100.0334 

104.9885 

33 

97.34343 

102.2970 

107.5356 

113.0753 

34 

104.1840 

109.6906 

115.5255 

121.7079 

35 

111.4351 

117.5462 

124.0346 

130.9232 

36 

119.1212 

125.8928 

133.0969 

140.7605 

37 

127.2684 

134.7611 

142.7481 

151.2618 

38 

135.9045 

144.1837 

153.0267 

162.4718 

39 

145.0588 

154.1950 

163.9735 

174.4388 

40 

154.7625 

164.8323 

175.6317 

187.2135 

41 

165.0483 

176.1344 

188.0477 

200.8504 

42 

175.9511 

188.1427 

201.2709 

215.4079 

43 

187.5083 

200.9016 

215.3535 

230.9479 

44 

199.7588 

214.4580 

230.3515 

247.5369 

45 

212.7443 

228.8615 

246.3243 

265.2456 

46 

226.5090 

244.1654 

263.3354 

284.1496 

47 

241.0995 

260.4258 

281.4523 

304.3298 

48 

256.5657 

277.7024 

300.7470 

325.8720 

49 

272.9595 

296.0587 

321.2954 

348.8684 

50 

290.3371 

315.5622 

343.1794 

373.4170 


.85 





Rate, 6% to 6%% 
Years, 51 to 75 


TABLE II 


ANNUITY FOR INVESTMENT 


The value of $1 invested at the end of every year at a fixed rate of 
compound interest for one to one hundred years. 


Years 

6% 



6%% 

51 

308.7573 

336.2848 

366.4860 

399.6227 

52 

328.2828 

358.3026 

391.3074 

427.5972 

53 

348.9797 

381.6965 

417.7425 

457.4600 

54 

370.9185 

406.5525 

445.8959 

489.3387 

55 

394.1737 

432.9620 

475.8789 

523.3692 

56 

418.8242 

461.0221 

507.8111 

559.6966 

57 

444.9537 

490.8358 

541.8188 

598.4762 

58 

472.6508 

522.5131 

578.0371 

639.8732 

59 

502.0100 

556.1701 

616.6095 

684.0647 

60 

533.1307 

591.9306 

657.6891 

731.2390 

61 

566.1185 

630.0222 

701.4388 

781.5976 

62 

601.0857 

670.2965 

748.0325 

835.3556 

63 

638.1508 

713.1899 

797.6543 

892.7421 

64 

677.4400 

758.7643 

850.5018 

954.0022 

65 

719.0865 

807.1869 

906.7846 

1019.397 

66 

763.2317 

858.6360 

966.7255 

1089.207 

67 

810.0257 

913.3006 

1030.563 

1163.728 

68 

859.9607 

971.3817 

1098.549 

1243.280 

69 

912.2050 

1033.093 

1170.955 

1328.201 

70 

967.9375 

1098.661 

1248.067 

1418.855 

71 

1027.014 

1168.328 

1330.191 

1515.627 

72 

1089.635 

1242.348 

1417.654 

1618.933 

73 

1156.013 

1320.995 

1510.800 

1729.210 

74 

1226.374 

1404.557 

1610.002 

1846.932 

75 

1300.957 

1493.341 

86 

1715.652 

1972.600 




TABLE II 


Rate, 6%?^ to 9 % 
Years, 76 to 100 


ANNUITY FOR INVESTMENT 


The value of $1 invested at the end of every year at a 
compound interest for one to one hundred years. 

fixed rate of 

Years 

6% 

61/4% 


6%% 

76 

1380.014 

1587.675 

1828.171 

2106.750 

77 

1463.815 

1687.904 

1948.002 

2249.956 

78 

1552.644 

1794.397 

2075.622 

2402.828 

79 

1646.803 

1907.547 

2211.537 

2566.019 

80 

1746.610 

2027.771 

2356.286 

2740.227 

81 

1852.407 

2155.506 

2510.445 

2926.193 

82 

1964.552 

2291.224 

2674.625 

3124.713 

83 

2083.423 

2435.426 

2849.475 

3336.630 

84 

2209.430 

2588.638 

3035.691 

3562.852 

85 

2342.997 

2751.429 

3234.011 

3804.348 

86 

2484.577 

2924.392 

3445.222 

4062.138 

87 

2634.652 

3108.166 

3670.163 

4337.332 

88 

2793.732 

3303.427 

3909.723 

4931.102 

89 

2962.355 

3510.891 

4164.854 

4944.702 

90 

3141.097 

3731.322 

4436.569 

5279.470 

91 

3330.563 

3965.530 

4725.946 

5636.834 

92 

3531.397 

4214.374 

5034.132 

6018.320 

93 

3744.282 

4478.773 

5362.351 

6425.557 

94 

3969.938 

4759.696 

5711.903 

6860.280 

95 

4209.135 

5058.176 

6084.177 

7324.353 

96 

4462.683 

5375.312 

6480.648 

7819.747 

97 

4731.445 

5712.269 

6902.889 

8348.579 

98 

5016.332 

6070.285 

7352.578 

8913.108 

99 

5318.312 

6450.677 

7831.495 

9515.744 

100 

5638.412 

6854.842 

8341.541 

10159.06 


87 






Rate, 7 %% 

'•^Yeara,' l,to 25 


TABLE II 


ANNUITY FOR INVESTMENT 


The value of $1 invested at the end of every year at a fixed rate of 
compound interest for one to one hundred years. 


Years 

l°lo^ 

7%% 

71 / 2 % 

7%% 

1 

1.000000 

1.000000 

1.000000 

1.000000 

2 

2.070000 

2.072492 

2.075000 

2.077497 

3 

3.214900 

3.222745 

3.230613 

3.238503 

4 

4.439943 

4.456400 

4.472920 

4.489484 

5 

5.750728 

5.779490 

5.808386 

5.837432 

6 

7.153285 

7.198498 

7.244026 

7.289832 

7 

8.654014 

8.720386 

8.787333 

8.854800 

8 

10.25981 

10.35262 

10.44638 

10.54105 

9 

11.97800 

12.10319 

12.22968 

12.35797 

10 

13.81645 

13.98068 

14.14711 

14.31572 

11 

15.78361 

15.99428 

16.20813 

16.42519 

12 

17.88846 

18.15386 

18.42374 

18.69815 

13 

20.14066 

20.47001 

20.80553 

21.14726 

14 

22.55050 

22.95410 

23.36596 

23.78617 

15 

25.12904 

25.61828 

26.11840 

26.62959 

16 

27.88808 

28.47560 

29.07729 

29.69338 

17 

30.84025 

31.54008 

32.25809 

32.99462 

18 

33.99907 

34.82673 

35.67745 

36.55170 

19 

37.37901 

38.35167 

39.35326 

40.38446 

20 

40.99554 

42.13215 

43.30476 

44.51427 

21 

44.86523 

46.18673 

47.55263 

48.96413 

22 

49.00580 

50.53527 

52.11908 

53.75885 

23 

53.43621 

55.19908 

57.02801 

58.92517 

24 

58.17675 

60.20101 

62.30512 

64.49188 

25 

63.24914 

65.56559 

67.97801 

70.49001 


88 




TABLE II 

ANNUITY FOR INVESTMENT 


Rale, 7% to 7%%- 
Years, 26 to 50 


The value of $1 invested at the end of every year at a fixed rate of 
compound interest for one to one hundred years. 


Years 

7% 

7%% 

7%% 

7%% 

26 

68.67658 

71.31909 

74.07639 

76.95299 

27 

74.48394 

77.48972 

80.63212 

83.91685 

28 

80.69783 

84.10772 

87.67953 

91.42040 

29 

87.34667 

91.20553 

95.25550 

99.50548 

30 

94.46094 

98.81793 

103.3997 

108.2172 

31 

102.0732 

106.9822 

112.1547 

117.6040 

32 

110.2183 

115.7384 

121.5663 

127.7183 

33 

118.9336 

125.1295 

131.6837 

138.6165 

34 

128.2590 

135.2014 

142.5600 

150.3587 

35 

138.2371 

146.0034 

154.2520 

163.0121 

36 

148.9137 

157.5887 

166.8209 

176.6455 

37 

160.3377 

170.0139 

180.3325 

191.3356 

38 

172.5614 

183.3401 

194.8574 

207.1641 

39 

185.6407 

197.6323 

210.4719 

224.2193 

40 

199.6356 

212.9604 

227.2573 

242.5964 

41 

214.6101 

229.4000 

245.3016 

262.3975 

42 

230.6327 

247.0314 

264.6992 

283.7334 

43 

247.7771 

265.9412 

285.5517 

306.7227 

44 

266.1215 

286.2219 

307.9681 

331.4938 

45 

285.7501 

307.9731 

332.0657 

358.1846 

46 

306.7526 

331.3011 

357.9707 

386.9440 

47 

329.2253 

356.3204 

385.8184 

417.9321 

48 

353.2710 

383.1538 

415.7551 

451.3219 

49 

379.0000 

411.9324 

447.9370 

487.2994 

50 

406.5300 

442.7975 

482.5320 

526.0652 


89 





Rate, 7% to 7%% 
Years, 51 to 75 


TABLE II 


ANNUITY FOR INVESTMENT 


The value of $1 invested at the end of every year at a fixed rate of 
oompound interest for one to one hundred years. 


Years 

7% 

7Vi<fo 

7%% 

7%fo 

51 

435.9871 

475.9003 

519.7222 

567.8352 

52 

467.5063 

511.4030 

559.7011 

612.8424 

53 

501.2317 

549.4797 

602.6787 

661.3378 

54 

537.3180 

590.3170 

648.8796 

713.5916 

55 

575.9303 

634.1150 

698.5456 

769.8950 

56 

617.2454 

681.0884 

751.9365 

830.5618 

57 

661.4527 

731.4673 

809.3319 

895.9305 

58 

708.7543 

785.4988 

871.0320 

966.3652 

59 

759.3671 

843.4474 

937.3595 

1042.258 

60 

813.5229 

905.5974 

1008.661 

1124.034 

61 

871.4694 

972.2532 

1085.311 

1212.146 

62 

933.4724 

1043.742 

1167.710 

1307.088 

63 

999.8156 

1120.413 

1256.288 

1409.387 

64 

1070.803 

1202.643 

1351.509 

1519.614 

65 

1146.759 

1290.834 

1453.872 

1638.385 

66 

1228.032 

1385.419 

1563.913 

1766.360 

67 

1314.994 

1486.862 

1682.207 

1904.253 

68 

1408.044 

1595.659 

1809.372 

2052.832 

69 

1507.607 

1712.345 

1946.076 

2212.926 

70 

1614.139 

1837.491 

2093.032 

2385.428 

71 

1728.130 

1971.709 

2251.009 

2571.299 

72 

1850.099 

2115.658 

2420.836 

2771.575 

73 

1980.606 

2270.043 

2603.399 

2987.373 

74 

2120.249 

2435.621 

2799.655 

3219.894 

75 

2269.666 

2613.203 

3010.628 

3470.436 


90 





TABLE 11 


Rate, 7% to 7%% 
Yean, 76 to 100 


ANNUITY FOR INVESTMENT 

The value of $1 invested at the end of every year at a fixed rate of 


compound interest for one to one hundred years. 

Years 

7% 

71 / 4 % 


m^o 

76 

2429.543 

2803.661 

3237.425 

3740.395 

77 

2600.611 

3007.926 

3481.232 

4031.276 

78 

2783.654 

3227.000 

3743.325 

4344.701 

79 

2979.510 

3461.959 

4025.075 

4682.414 

80 

3189.076 

3713.950 

4327.955 

5046.302 

81 

3413.311 

3984.212 

4653.552 

5438.391 

82 

3653.244 

4274.068 

5003.569 

5860.866 

83 

3909.969 

4584.937 

5379.837 

6316.083 

84 

4184.669 

4918.345 

5784.325 

6806.579 

85 

4478.596 

5275.924 

6219.151 

7335.090 

86 

4793.099 

5659.429 

6686.588 

7904.560 

87 

5129.616 

6070.738 

7189.083 

8518.164 

88 

5489.689 

6511.866 

7729.264 

9179.323 

89 

5874.969 

6984.977 

8309.960 

9891.721 

90 

6287.214 

7492.388 

8934.208 

10659.33 

91 

6728.320 

8036.586 

9605.275 

11486.43 

92 

7200.303 

8620.239 

10326.67 

12377.63 

93 

7705.324 

9246.206 

11102.17 

13337.90 

94 

8245.697 

9917.554 

11935.84 

14372.58 

95 

8823.896 

10637.58 

12832.03 

15487.46 

96 

9442.568 

11409.80 

13795.43 

16688.74 

97 

10104.55 

12138.01 

14831.08 

17983.11 

98 

10812.87 

13126.27 

15944.41 

19377.81 

99 

11570.77 

14078.93 

17141.24 

20880.59 

100 

12381.73 

15100.65 

18427.84 

22499.83 


91 





Rate/ 8% to 8%% 
Years, 1 to 25 


TABLE II 


ANNUITY FOR INVESTMENT 


The value of $1 invested at the end of every year at a fixed rate of 
compound interest for one to one hundred years. 


Years 

8 % 

8 %% 

81/2 

8 %% 

1 

1.000000 

1.000000 

1.000000 

1.000000 

2 

2.080000 

2.082497 

2.085000 

2.087497 

3 

3.246400 

3.254303 

3.262222 

3.270160 

4 

4.506112 

4.522788 

4.539505 

4.556297 

5 

5.866600 

5.895915 

5.925364 

5.954971 

6 

7.335937 

7.382327 

7.429011 

7.476034 

7 

8.922812 

8.991370 

9.060482 

9.130194 

8 

10.63664 

10.73316 

10.83062 

10.92909 

9 

12.48757 

12.61864 

12.75121 

12.88538 

10 

14.48653 

14.65968 

14.83507 

15.01286 

11 

16.64551 

16.86912 

17.09605 

17.32648 

12 

18.97716 

19.26081 

19.54921 

19.84255 

13 

21.49534 

21.84983 

22.21089 

22.57878 

14 

24.21497 

24.65244 

25.09881 

25.55442 

15 

27.15216 

27.68625 

28.23221 

28.79045 

16 

30.32433 

30.97036 

31.63195 

32.30961 

17 

33.75028 

34.52542 

35.32066 

36.13670 

18 

37.45031 

38.37377 

39.32291 

40.29866 

19 

41.44633 

42.53960 

43.66536 

44.82480 

20 

45.76207 

47.04912 

48.37690 

49.74698 

21 

50.42304 

51.93067 

53.48894 

55.09985 

22 

55.45690 

57.21495 

59.03549 

60.92109 

23 

60.89345 

62.93518 

65.05352 

67.25169 

24 

66.76494 

69.12733 

71.58306 

74.13622 

25 

73.10614 

75.83034 

78.66759 

81.62315 


92 





TABLE II 

ANNUITY FOR INVESTMENT 


Rate, 8 % to 8%% 
Years, 26 to 50 


The value of $1 invested at the end of every year at a fixed rate of 
compound interest for one to one hundred years. 


Years 

81/4% 

81/2% 

8 %% 

8 % 

26 

79.95642 

83.08634 

86.35434 

89.76518 

27 

87.35100 

90.94096 

94.69446 

98.61963 

28 

95.33907 

99.44359 

103.7434 

108.2488 

29 

103.9662 

108.6477 

113.5616 

118.7207 

30 

113.2835 

118.6112 

124.2144 

130.1088 

31 

123.3462 

129.3966 

135.7726 

142.4934 

32 

134.2139 

141.0718 

148.3133 

155.9615 

33 

145.9510 

153.7102 

161.9198 

170.6081 

34 

158.6271 

167.3913 

176.6829 

186.5363 

35 

172.3174 

182.2010 

192.7009 

203.8582 

36 

187.1029 

198.2326 

210.0806 

222.6958 

37 

203.0710 

215.5868 

228.9374 

243.1818 

38 

220.3167 

234.3727 

249.3971 

265.4602 

39 

238.9422 

254.7085 

271.5957 

289.6880 

40 

259.0576 

276.7219 

295.6814 

316.0358 

41 

280.7822 

300.5515 

321.8143 

344.6889 

42 

304.2449 

326.3469 

350.1684 

375.8493 

43 

329.5845 

354.2705 

380.9327 

409.7360 

44 

356.9512 

384.4978 

414.3120 

446.5880 

45 

386.5074 

417.2189 

450.5284 

486.6645 

46 

418.4280 

452.6395 

489.8234 

530.2477 

47 

452.9022 

490.9823 

532.4584 

577.6443 

48 

490.1345 

532.4882 

578.7173 

629.1882 

49 

530.3454 

577.4185 

628.9081 

685.2423 

50 

573.7731 

626.0555 

683.3653 

746.2010 


93 





Rate, S% to 
Years, 51 to 75 


TABLE II 


ANNUITY FOR INVESTMENT 


The value of $1 invested at the end of every year at a fixed rate of 
compound interest for one to one hundred years. 


Years 

8% 



8%% 

51 

620.6750 

678.7051 

742.4513 

812.4936 

52 

671.3290 

735.6983 

806.5595 

884.5867 

53 

726.0354 

797.3935 

876.1171 

962.9881 

54 

785.1183 

864.1784 

951.5869 

1048.250 

55 

848.9279 

936.4732 

1033.472 

1140.972 

56 

917.8421 

1014.732 

1122.317 

1241.807 

57 

992.2695 

1099.448 

1218.713 

1351.465 

58 

1072.651 

1191.152 

1323.304 

1470.719 

59 

1159.463 

1290.422 

1436.785 

1600.407 

60 

1253.221 

1397.881 

1559.911 

1741.442 

61 

1354.479 

1514.206 

1693.504 

1894.818 

62 

1463.837 

1640.128 

1838.452 

2061.615 

63 

1581.945 

1776.440 

1995.720 

2243.007 

64 

1709.500 

1923.996 

2166.355 

2440.271 

65 

1847.260 

2083.726 

2351.495 

2654.794 

66 

1996.041 

2256.634 

2552.372 

2888.089 

67 

2156.725 

2443.806 

2770.324 

3141.798 

68 

2330.264 

2646.419 

3006.801 

3417.705 

69 

2517.685 

2865.749 

3263.379 

3717.754 

70 

2720.100 

3103.173 

3541.766 

4044.058 

71 

2938.709 

3360.185 

3843.816 

4398.913 

72 

3174.805 

3638.400 

4171.541 

4784.818 

73 

3429.790 

3939.567 

4527.121 

5204.490 

74 

3705.174 

4265.582 

4912.925 

5660.883 

75 

4002.588 

4618.492 

5331.524 

6157.211 


94 




TABLE II 


Rate, 8% to &%% 
Year*, 76 to 106 


ANNUITY FOR INVESTMENT 


The value of $1 invested at the end of every year at a fixed rate of 
compound interest for one to one hundred years. 

Years 

8% 

81/4% 

8y2% 

8%% 

76 

4323.795 

5000.518 

5785.702 

6696.968 

77 

4670.699 

5414.061 

6278.486 

7283.954 

78 

5045.354 

5861.720 

6813.156 

7922.301 

79 

5449.983 

6346.313 

7393.274 

8616.503 

80 

5886.981 

6870.884 

8022.701 

9371.447 

81 

6358.940 

7438.731 

8705.631 

10192.45 

82 

6868.656 

8053.427 

9446.609 

11085.29 

83 

7419.150 

8718.834 

10250.57 

12056.25 

84 

8013.684 

9439.137 

11122.87 

13112.17 

85 

8655.780 

10218.87 

12069.31 

14260.49 

86 

9349.243 

11062.92 

13096.20 

15509.28 

87 

10098.18 

11976.61 

14210.38 

16867.34 

88 

10907.03 

12965.68 

15419.26 

18344.24 

89 

11780.60 

14036.35 

16730.89 

19950.37 

90 

12724.05 

15195.35 

18154.01 

21697.03 

91 

13742.97 

16449.96 

19698.11 

23596.03 

92 

14843.41 ' 

17808.08 

21373.45 

25662.21 

93 

16031.89 

19278.25 

23191.19 

27908.67 

94 

17315.44 

20869.72 

25163.44 

30351.68 

95 

18701.67 

22592.47 

27303.32 

33008.45 

96 

20198.81 

24437.36 

29625.10 

35897.69 

97 

21815.72 

26476.08 

32144.23 

39039.74 

98 

23561.99 

28661.35 

34877.49 

42456.73 

99 

25447.95 

31026.91 

37843.07 

46172.70 

100 

27484.79 

33587.62 

41060.73 

50213.81 


95 




Rate, 9% to 9%% 
Years, 1 to 25 


TABLE II 


ANNUITY FOR INVESTMENT 


The value of $1 invested at the end'of every year at a fixed rate of 
compound interest for one to one hundred years. 


Years 

9% 

9%% 

91 / 2 % 

9%% 

1 

1.000000 

1.000000 

1.000000 

1.000000 

2 

2.090000 

2.092497 

2.095000 

2.097497 

3 

3.278100 

3.286054 

3.294021 

3.202000 

4 

4.573122 

4.590011 

4.606958 

4.623949 

5 

5.984700 

6.014584 

6.044610 

6.074779 

6 

7.523333 

7.570930 

7.618842 

7.667067 

7 

9.200433 

9.271243 

9.342631 

9.414605 

8 

11.02846 

11.12883 

11.23019 

11.33253 

9 

13.02103 

13.15825 

13.29706 

13.43746 

10 

15.19292 

15.37537 

11.56027 

15.74760 

11 

17.56029 

17.79759 

18.03851 

18.28299 

12 

20.14072 

20.44387 

20.75216 

21.06558 

13 

22.95337 

23.33493 

23.72361 

24.11948 

14 

26.01917 

26.49341 

26.97735 

27.47113 

15 

29.36091 

29.94403 

30.54021 

31.14956 

16 

33.00339 

33.71385 

34.44152 

35.18664 

17 

36.97370 

37.83238 

38.71347 

39.61732 

18 

41.30133 

42.33187 

43.39125 

44.48001 

19 

46.01845 

47.24757 

48.51342 

49.81681 

20 

51.16012 

52.61797 

54.12217 

55.67394 

21 

56.76453 

58.48510 

60.26378 

62.10214 

22 

62.87334 

64.89497 

66.98883 

69.15711 

23 

69.53194 

71.89775 

74.35277 

76.89993 

24 

76.78982 

79.54828 

82.41627 

85.39767 

25 

84.70091 

87.90649 

91.24581 

94.72390 


96 




TABLE II 


Rate, 9% to 9%% 
Years, 26 to 50 


ANNUITY FOR INVESTMENT 


The value of $1 invested at the end of every year at 
compound interest for one to one hundred years. 

a fixed rate c 

Years 

9% 

91 / 4 % 

91 / 2 % 

9 %% 

26 

93.32400 

97.03784 

100.9142 

104.9595 

27 

102.7231 

107.0137 

111.5010 

116.1930 

28 

112.9682 

117.9126 

123.0936 

128.5216 

29 

124.1353 

129.8195 

135.7875 

142.0527 

30 

136.3074 

142.8278 

149.6872 

156.9029 

31 

149.5751 

157.0394 

164.9076 

173.2009 

32 

164.0369 

172.5655 

181.5738 

191.0880 

33 

179.8002 

189.5278 

199.8233 

210.7191 

34 

196.9823 

208.0590 

219.8065 

232.2641 

35 

215.7107 

228.3044 

241.6881 

255.9098 

36 

236.1248 

250.4226 

265.6484 

281.8610 

37 

258.3759 

274.5865 

291.8850 

310.3424 

38 

282.6298 

300.9858 

320.6137 

341.6007 

39 

309.0664 

329.8270 

352.0723 

375.9069 

40 

337.8824 

361.3360 

386.5192 

413.5577 

41 

369.2919 

395.7596 

424.2385 

454.8796 

42 

403.5282 

433.3672 

465.5411 

500.2303 

43 

440.8458 

474.4536 

510.7675 

550.0027 

44 

481.5219 

519.3406 

560.2904 

604.6279 

45 

525.8589 

568.3795 

614.5180 

664.5791 

46 

574.1862 

621.9545 

673.8972 

730.3755 

47 

626.8628 

680.4853 

738.9174 

802.5869 

48 

684.2806 

744.4301 

810.1145 

881.8393 

49 

746.8658 

814.2897 

888.0754 

968.8186 

50 

815.0837 

890.6115 

973.4425 

1074.278 


12 

97 






Rate, 9 % to 9%®^ 
Years, 51 to 75 


TABLE II 

ANNUITY FOR INVESTMENT 


The value of $1 invested at the end of every year at a fixed rate of 
compound interest for one to one hundred years. 


Years 

9% 

91 / 4 % 

91 / 2 % 


51 

889.4412 

973.9930 

1066.920 

1169.045 

52 

970.4909 

1065.087 

1169.277 

1284.028 

53 

1058.835 

1164.608 

1281.359 

1410.221 

54 

1155.130 

1273.334 

1404.087 

1548.716 

55 

1260.092 

1392.117 

1538.475 

1700.716 

56 

1374.500 

1521.888 

1685.631 

1867.535 

57 

1499.205 

1663.662 

1846.765 

2050.619 

58 

1635.133 

1818.549 

2023.207 

2251.555 

59 

1783.295 

1987.765 

2216.411 

2472.082 

60 

1944.792 

2172.634 

2427.971 

2714.109 

61 

2120.823 

2374.602 

2659.628 

2979.734 

62 

2312.699 

2595.253 

2913.293 

3271.258 

63 

2521.842 

2836.314 

3191.055 

3591.206 

64 

2749.808 

3099.672 

3495.205 

3942.349 

65 

2998.290 

3387.392 

3828.251 

4327.727 

66 

3269.137 

3701.725 

4192.935 

4750.680 

67 

3564.358 

4045.135 

4592.263 

5214.870 

68 

3886.150 

4420.309 

5029.527 

5724.320 

69 

4236.903 

4830.187 

5508.332 

6283.441 

70 

4619.224 

5277.978 

6032.623 

6897.076 

71 

5035.956 

5767.191 

6606.722 

7570.541 

72 

5490.191 

6301.656 

7235.361 

7309.669 

73 

5985.308 

6885.559 

7923.720 

9120.862 

74 

6524.986 

7523.472 

8677.474 

10011.15 

75 

7113.234 

8220.391 

9502.834 

10988.23 


98 




TABLE II 


Rate, 9% to 9 %% 
Year*, 76 to 100 


ANNUITY FOR INVESTMENT 


The value of $1 invested at the end of every year at a fixed rate of 


compound interest for one to one hundred years. 

Years 

9% 


9%% 

9%% 

76 

7754.425 

8981.777 

10406.60 

12060.57 

77 

8453.324 

9813.591 

11396.23 

13237.49 

78 

9215.123 

10722.35 

12479.87 

14529.14 

79 

10045.48 

11715.16 

13666.46 

15946.73 

80 

10950.58 

12799.81 

14965.77 

17502.53 

81 

11937.14 

13984.79 

16388.52 

19210.03 

82 

13012.47 

15279.38 

17946.42 

21084.01 

83 

14184.59 

16693.72 

19652.34 

23140.70 

84 

15462.20 

18238.89 

21520.31 

25397.91 

85 

16854.80 

19926.98 

23565.73 

27875.20 

86 

18372.73 

21771.23 

25805.47 

30594.04 

87 

20027.28 

23786.06 

28257.99 

33577.95 

88 

21830.73 

25987.28 

30943.51 

36852.81 

89 

23796.50 

28392.10 

33884.14 

40446.94 

90 

25939.19 

31019.36 

37104.12 

44391.53 

91 

28274.72 

33889.65 

40630.01 

48720.70 

92 

30820.44 

37025.44 

44490.86 

53471.96 

93 

33595.29 

40451.29 

48718.49 

58686.47 

94 

36619.87 

44194.03 

53347.76 

64409.41 

95 

39916.64 

48282.97 

58416.79 

70690.31 

96 

43510.14 

52750.14 

63967.37 

77583.61 

97 

47427.07 

57630.53 

70045.28 

85148.91 

98 

51693.18 

62962.34 

76700.58 

93451.94 

99 

56350.18 

68787.35 

83988.12 

102564.6 

100 

61422.70 

75151.17 

91968.00 

112565.6 


99 




0'< 


TABLE III 


ANNUITY FOR INSTALMENT 

1 ) 

^ <f—1 


The annuity or annual instalment which will amortize a capital of $1. for 
one to one hundred years at the following rates of interest. 


1% 

1%% 

11/2% 

1%% 

2% 

2V4% 

2-V^% 

2%% 



31/2% 

3%% 


4% 9^ 

4%% 

4%% 

5% 

51/4% 

51/2% 


6% 

61/4% 

6%% 

6%% 

l°lo 

71/4% 

71/2% 

7%% 

8% 

81/4% 

8%%- 

8%<fo 

9% 


91/2% 

9%% 


EXAMPLE.—What is the annuity payable every year which amortizes a 
capital of $1000 in seventy-seven years, @ per annum compound interest? 

C=1000. <7=1.0425. n=77 <f=1.0425^^ 


Therefore 


. c<7"(<r-l) 

< 7^—1 


1000X1.0425^^(1.0425—1) 

1.0425^^—1 


Table I page 33 shows that 1.0425’'^ or $1, invested @ 4^% per annum 
compound interest, for seventy-seven years, becomes 24.65243; therefore the 
equation will read: 

1000 X24.65243 X0.0425-f-23.65243=$44.29685 

Also Table III, page 117, shows that the annuity or the annual equal instal¬ 
ment which will amortize a capital of $1, in 77 years, @ 4^% per annum is 
0.04429685 ; therefore for $1000 will be: 0.4429685 X1000=$44.29685. 

101 







Rate, 1% to 1%% 
Years, 1 to 2S 


TABLE III 

ANNUAL INSTALMENT 


The annuity which will amortize a capital of $1 at a fixed rate of compound 
interest for one to one hundred years. 


Years 

Ifo 

1 %% 

1 %% 

1 %% 

1 

1.0100000 

1.0125000 

1.0150000 

1.0175000 

2 

0.5075124 

0.5093993 

0.5112780 

0.5131666 

3 

0.3400221 

0.3417074 

0.3433856 

0.3450682 

4 

0.2562811 

0.2578625 

0.2594471 

0.2610324 

5 

0.2060400 

0.2075626 

0.2090893 

0.2106226 

6 

0.1725487 

0.1740342 

0.1755273 

0.1770231 

7 

0.1486290 

0.1500895 

0.1515573 

0.1530308 

8 

0.1306898 

0.1321333 

0.1335854 

0.1350428 

9 

0.1167406 

0.1181707 

0.1196112 

0.1210582 

10 

0.1055821 

0.1070037 

0.1084352 

0.1098756 

11 

0.09645360 

0.09786912 

0.09929477 

0.1007303 

12 

0.08884880 

0.09025904 

0.09168084 

0.09310410 

13 

0.08241444 

0.08382142 

0.08524082 

0.08667296 

14 

0.07690082 

0.07830574 

0.07972382 

0.08115582 

15 

0.07212338 

0.07352680 

0.07494485 

0.07637753 

16 

0.06794415 

0.06934713 

0.07076563 

0.07219965 

17 

0.06425789 

0.06566049 

0.06708008 

0.06851640 

18 

0.06098190 

0.06238506 

0.06380620 

0.06524493 

19 

0.05805151 

0.05945575 

0.06087886 

0.06232077 

20 

0.05541523 

0.05682074 

0.05824611 

0.05969134 

21 

0.05303057 

0.05443771 

0.05586580 

0.05731479 

22 

0.05086351 

0.05227271 

0.05370370 

0.05515650 

23 

0.04888558 

0.05029690 

0.05173112 

0.05318806 

24 

0.04707329 

0.04848684 

0.04992439 

0.05138577 

25 

0.04540663 

0.04682267 

0.04826375 

0.04962960 


102 




TABLE III 


Rate. 1% to 1%% 
Yemr», 26 to 50 


ANNUAL INSTALMENT 


The annuity which will amortize a capital of $1 at a fixed rate of compound 
interest for one to one hundred years. 


Years 

1% 

1%% 

11 / 2 % 

1%% 

26 

0.04386869 

0.04528748 

0.04673225 

0.04818329 

27 

0.04244541 

0.04386700 

0.04531552 

0.04679090 

28 

0.04112433 

0.04254886 

0.04400131 

0.04548159 

29 

0.03989492 

0.04132249 

0.04277902 

0.04426430 

30 

0.03874794 

0.04017876 

0.04163943 

0.04312984 

31 

0.03767561 

0.03910961 

0.04057449 

0.04207013 

32 

0.03667072 

0.03810810 

0.03957726 

0.04107820 

33 

0.03572731 

0.03716807 

0.03864164 

0.04014786 

54 

0.03483985 

0.03628407 

0.03776207 

0.03927374 

3^- 

0.03400355 

0.03545127 

0.03693383 

0.03845090 

36 

0.03321418 

0.03466548 

0.03615260 

0.03767513 

37 

0.03246792 

0.03392285 

0.03541456 

0.03694263 

38 

0.03176136 

0.03322001 

0.03471635 

0.03624996 

39 

0.03109148 

0.03255381 

0.03405481 

0.03559405 

40 

0.03045546 

0.03192154 

0.03342728 

0.03497216 

41 

0.02985093 

0.03132076 

0.03283123 

0.03438177 

42 

0.02927551 

0.03074919 

0.03226440 

0.03382062 

43 

0.02872726 

0.03020478 

0.03172480 

0.03328672 

44 

0.02820429 

0.02968570 

0.03121052 

0.03277815 

45 

0.02770491 

0.02919025 

0.03071951 

0.03229326 

46 

0.02722763 

0.02871688 

0.03025140 

0.03183048 

47 

0.02677101 

0.02826418 

0.02980358 

0.03138841 

48 

0.02633373 

0.02783088 

0.02937514 

0.03096574 

49 

0.02591465 

0.02741576 

0.02896492 

0.03056130 

50 

0.02551263 

0.02701773 

0.02857183 

0.03017397 


. 103 




Rate, 1% to 1%X 
Years, 51 to 75 


TABLE III 

ANNUAL INSTALMENT 


The annuity which will amortize a capital of $1 at a fixed rate of coniponnd 
interest for one to one hundred years. 


Years 

1 % 

l%fo 

IVsYc 

1%^0 

51 

0.02512670 

0.02663584 

0.02819481 

0.02980276 

52 

0.02475592 

0.02626907 

0.02783300 

0.02944668 

53 

0.02439947 

0.02591665 

0.02748550 

0.02910497 

54 

0.02405648 

0.02557771 

0.02715151 

0.02877677 

55 

0.02372627 

0.02525155 

0.02583030 

0.02846133 

56 

0.02340821 

0.02493747 

0.02652118 

0.02815798 

57 

0.02310145 

0.02463487 

0.02622351 

0.02786611 

58 

0.02280564 

0.02434312 

0.02593673 

0.02758508 

59 

0.02252011 

0.02406168 

0.02566023 

0.02731434 

60 

0.02224435 

0.02379003 

0.02539354 

0.02705341 

61 

0.02197791 

0.02352767 

0.02513615 

0.02680177 

62 

0.02172032 

0.02327419 

0.02488761 

0.02655895 

63 

0.02147116 

0.02302912 

0.02464751 

0.02632458 

64 

0.02123005 

0.02279212 

0.02441544 

0.02609825 

65 

0.02099659 

0.02256276 

0.02419104 

0.02587954 

66 

0.02077044 

0.02234073 

0.02397396 

0.02566818 

67 

0.02055129 

0.02212570 

0.02376384 

0.02546376 

78 

0.02033881 

0.02191733 

0.02356041 

0.02526600 

69 

0.02013272 

0.02171534 

0.02336337 

0.02507462 

70 

0.01993274 

0.02151948 

0.02317244 

0.02488933 

71 

0.01973862 

0.02132948 

0.02298735 

0.02470988 

72 

0.01955011 

0.02114509 

0.02280787 

0.02453603 

73 

0.01936698 

0.02096607 

0.02263376 

0.02436752 

74 

0.01918903 

0.02079222 

0.02246481 

0.02420417 

75 

0.01901602 

0.02062333 

0.02230081 

0.02404573 


104 




TABLE III 


Rale, 1% to 1%% 
Year., 76 to 100 


ANNUAL INSTALMENT 


The annuity which will amortize a capital of $1 at a fixed rate of compound 
interest for one to one hundred years. 


Years 

1 % 


1 %% 

1 %% 

76 

0.01884776 

0.02045918 

0.02214154 

0.02389204 

77 

0.01868408 

0.02029961 

0.02198685 

0.02374288 

78 

0.01852481 

0.02014443 

0.02183653 

0.02359809 

79 

0.01836977 

0.01999346 

0.02169044 

0.02345750 

80 

0.01821878 

0.01984658 

0.02154840 

0.02332096 

81 

0.01807172 

0.01970362 

0.02141026 

0.02318830 

82 

0.01792845 

0.01956442 

0.02127589 

0.02305939 

83 

0.01778880 

0.01942888 

0.02114515 

0.02293408 

84 

0.01765267 

0.01929682 

0.02101791 

0.02281225 

85 

0.01751992 

0.01916814 

0.02089403 

0.02269377 

86 

0.01739043 

0.01904273 

0.02077340 

0.02257852 

87 

0.01726415 

0.01892047 

0.02065591 

0.02246638 

88 

0.01714084 

0.01880125 

0.02054144 

0.02235726 

89 

0.01702049 

0.01868496 

0.02042990 

0.02225105 

90 

0.01690299 

0.01857152 

0.02032120 

0.02214763 

91 

0.01678825 

0.01846082 

0.02021522 

0.02204693 

92 

0.01667617 

0.01835278 

0.02011188 

0.02194884 

93 

0.01656666 

0.01824729 

0.02001110 

0.02185329 

94 

0.01645966 

0.01814430 

0.01991279 

0.02176020 

95 

0.01635505 

0.01804371 

0.01981687 

0.02166946 

96 

0.01625279 

0.01794545 

0.01972327 

0.02158104 

97 

0.01615278 

0.01784946 

0.01963192 

0.02149482 

98 

0.01605498 

0.01775564 

0.01954274 

0.02141076 

99 

0.01595930 

0.01766395 

0.01945566 

0.02132878 

100 

0.01586569 

0.01757433 

105 

0.01937063 

0.02124881 




Rate. 2^ to 23/4%' 
Years. 1 to 25 


TABLE III 

ANNUAL INSTALMENT 


The annuity which will amortize a capital of $1 at a fixed rate of compound 
interest for one to one hundred years. 


Years 

2 % 

21/4% 

2 %% 

2 %% 

1 

1.0200000 

1.0225000 

1.0250000 

1.0275000 

2 

0.5150495 

0.5169405 

0.5188271 

0.5207204 

3 

0.3467545 

0.3484499 

0.3501397 

0.3518346 

4 

0.2626242 

0.2642224 

0.2658175 

0.2674211 

5 

0.2121598 

0.2137013 

0.2152471 

0.2167987 

6 

0.1785263 

0.1800354 

0.1815503 

0.1830711 

7 

0.1545134 

0.1560003 

0.1574952 

0.1589978 

8 

0.1365093 

0.1379853 

0.1394673 

0.1409582 

9 

0.1225152 

0.1239816 

0.1254569 

0.1269413 

10 

0.1113263 

0.1127878 

0.1142586 

0.1157400 

11 

0.1021777 

0.1036367 

0.1051058 

0.1065866 

12 

0.09455956 

0.09601762 

0.09748689 

0.09896882 

13 

0.08811828 

0.08957708 

0.09105481 

0.09253274 

14 

0.08260172 

0.08406256 

0.08553636 

0.08702472 

15 

0.07782537 

0.07928854 

0.08076622 

0.08225928 

16 

0.07365007 

0.07511682 

0.07659884 

0.07809724 

17 

0.06996976 

0.07144058 

0.07292762 

0.07443192 

18 

0.06670201 

0.06817739 

0.06966998 

0.07118075 

19 

0.06378169 

0.06526200 

0.06676050 

0.06827815 

20 

0.06115657 

0.06264217 

0.06414696 

0.06567186 

21 

0.05878465 

0.06027581 

0.06178720 

0.06331950 

22 

0.05663133 

0.05812833 

0.05964648 

0.06118648 

23 

0.05466799 

0.06617108 

0.05769627 

0.05924420 

24 

0.05287101 

0.05438035 

0.05591268 

0.05746873 

25 

0.05122033 

0.05273607 

0.05427583 

0.05584009 


106 




TABLE III 


Rate, 2% to 2%% 
Years, 26 to 50 


ANNUAL INSTALMENT 


The annuity which will amortize a capital of $1 at a fixed rate of compound 
interest for one to one hundred years. 


.. Years 

2 % 


2 y2% 

2%<fo 

26 

0.04969915 

0.05122144 

0.05276864 

0.05434126 

27 

0.04829299 

0.04982196 

0.05137678 

0.05295786 

28 

0.04698958 

0.04852536 

0.05008786 

0.05167748 

29 

0.04577828 

0.04732091 

0.04889119 

0.05048945 

30 

0.04464988 

0.04619940 

0.04777755 

0.04938450 

31 

0.04359629 

0.04515286 

0.04673890 

0.04835460 

32 

0.04261052 

0.04417421 

0.04576823 

0.04739272 

33 

0.04168651 

0.04325728 

0.04485930 

0.04649261 

34 

0.04081864 

0.04239662 

0.04400658 

0.04564882 

35 

0.04000212 

0.04158738 

0.04320549 

0.04485652 

36 

0.03923277 

0.04082528 

0.04245150 

0.04411138 

37 

0.03850669 

0.04010652 

0.04174083 

0.04340959 

38 

0.03782048 

0.03942762 

0.04107004 

0.04274771 

39 

0.03717106 

0.03878549 

0.04043608 

0.04212263 

40 

0.03655566 

0.03817741 

0.03983616 

0.04153159 

41 

0.03597181 

0.03760091 

0.03926781 

0.04097207 

42 

0.03541724 

0.03705369 

0.03872869 

0.04044181 

43 

0.03488987 

0.03653369 

0.03821683 

0.03993877 

44 

0.03438787 

0.03603906 

0.03773030 

0.03946105 

45 

0.03390955 

0.03556810 

0.03726744 

0.03900697 

46 

0.03345335 

0.03511926 

0.03682670 

0.03857498 

47 

0.03301785 

0.03469112 

0.03640663 

0.03816363 

48 

0.03260178 

0.03428236 

0.03600595 

0.03777161 

49 

0.03220390 

0.03389184 

0.03562342 

0.03739777 

50 

0.03182316 

0.03351840 

0.03525800 

0.03704098 


107 




Rale, 2% to 2%% 
Years, 51 to 75 


TABLE III 


ANNUAL INSTALMENT 

The annuity which will amortize a capital of $1 at a fixed rate of compound 
interest for one to one hundred years. 


Years 

2^0 

2 %% 

2 %% 


51 

0.03145851 

0.03316105 

0.03490865 

0.03670019 

52 

0.03110903 

0.03281886 

0.03457442 

0.03637449 

53 

0.03077386 

0.03249097 

0.03425444 

0.03606302 

54 

0.03045222 

0.03217657 

0.03394793 

0.03576496 

55 

0.03014333 

0.03187494 

0.03365414 

0.03547958 

56 

0.02984651 

0.03158534 

0.03337238 

0.03520617 

57 

0.02956115 

0.03130716 

0.03310198 

0.03494409 

58 

0.02928662 

0.03103984 

0.03284239 

0.03469275 

59 

0.02902240 

0.03078271 

0.03259303 

0.03445158 

60 

0.02876791 

0.03053536 

0.03235336 

0.03422007 

61 

0.02852274 

0.03029726 

0.03212291 

0.03399772 

62 

0.02828639 

0.03006798 

0.03190122 

0.03378407 

63 

0.02805844 

0.02984706 

0.03168786 

0.03357871 

64 

0.02783850 

0.02963413 

0.03148244 

0.03338122 

65 

0.02762620 

0.02942881 

0.03128460 

0.03319125 

66 

0.02742118 

0.02923072 

0.03109394 

0.03300840 

67 

0.02722311 

0.02903957 

0.03091019 

0.03283240 

68 

0.02703168 

0.02885502 

0.03073296 

0.03266289 

69 

0.02684661 

0.02867679 

0.03056202 

0.03249958 

70 

0.02666761 

0.02850461 

0.03039709 

0.03234221 

71 

0.02649442 

0.02833819 

0.03023788 

0.03219050 

72 

0.02632678 

0.02817731 

0.03008414 

0.03204424 

73 

0.02616451 

0.02802172 

0.02993566 

0.03190314 

74 

0.02600732 

0.02787121 

0.02979218 

0.03176701 

75 

0.02585505 

0.02772555 

0.02965354 

0.03163563 


108 




TABLE III 

ANNUAL INSTALMENT 


Rate, 2% to 2%,% 
Years, 76 to 100 


The annuity which will amortize a capial of $1 at a fixed rate of compound 
interest for one to one hundred years. 


Years 

2 % 

21/4% 

21 /2% 

2 %% 

76 

0.02570748 

0.02758458 

0.02951952 

0.03150881 

77 

0.02556443 

0.02744809 

0.02938993 

0.03138636 

78 

0.02542573 

0.02731591 

0.02926461 

0.03126809 

79 

0.02529120 

0.02718785 

0.02914335 

0.03115384 

80 

0.02516067 

0.02706377 

0.02902601 

0.03104345 

81 

0.02503402 

0.02694351 

0.02891245 

0.03093676 

82 

0.02491108 

0.02682694 

0.02880251 

0.03083362 

83 

0.02479170 

0.02671389 

0.02869606 

0.03073391 

84 

0.02467578 

0.02660424 

0.02859295 

0.03063748 

85 

0.02456317 

0.02649789 

0.02849308 

0.03054423 

86 

0.02445378 

0.02639468 

0.02839630 

0.03045401 

87 

0.02434746 

0.02629452 

0.02830252 

0.03036670 

88 

0.02424413 

0.02619731 

0.02821163 

0.03028220 

89 

0.02414369 

0.02610292 

0.02812350 

0.03020044 

90 

0.02404599 

0.02601128 

0.02803806 

0.03012127 

91 

0.02395097 

0.02592225 

0.02795521 

0.03004463 

92 

0.02385856 

0.02583578 

0.02778484 

0.02997040 

93 

0.02376863 

0.02575177 

0.02779688 

0.02989853 

94 

0.02368115 

0.02567013 

0.02772123 

0.02982892 

95 

0.02359598 

0.02559079 

0.02764783 

0.02976143 

96 

0.02351310 

0.02551366 

0.02757660 

0.02969607 

97 

0.02343240 

0.02543869 

0.02750744 

0.02963273 

98 

0.02335381 

0.02536579 

0.02744032 

0.02957135 

99 

0.02327727 

0.02529489 

0.02737514 

0.02951185 

100 

0.02320273 

0.02522594 

109 

0.02731186 

0.02945419 




Rate, ZXto 3%% 
Years, 1 to 25 


TABLE III 

ANNUAL INSTALMENT 


The annuity which will amortize a capital of $1 at a fixed rate of compound 
interest for one to one hundred years. 


Years 


3%% 

31 / 2 % 

3%% 

1 

1.0300000 

1.0325000 

1.0350000 

1.0375000 

2 

0.5226108 

0.5245066 

0.5264011 

0.5282991 

3 

0.3535303 

0.3552313 

0.3569367 

0.3586387 

4 

0.2690271 

0.2706371 

0.2722527 

0.2738679 

5 

0.2183546 

0.2199149 

0.2214827 

0.2230517 

6 

0.1845985 

0.1861294 

0.1876691 

0.1892119 

7 

0.1605068 

0.1620219 

0.1635451 

0.1650735 

8 

0.1424568 

0.1439626 

0.1454773 

0.1469983 

9 

0.1284342 

0.1299356 

0.1314464 

0.1329650 

10 

0.1172308 

0.1187309 

0.1202417 

0.1217613 

11 

0.1080776 

0.1095793 

0.1110924 

0.1126152 

12 

0.1004622 

0.1019670 

0.1034845 

0.1050122 

13 

0.09402979 

0.09553909 

0.09706190 

0.09859632 

14 

0.08852656 

0.09004158 

0.09157104 

0.09311306 

15 

0.08376672 

0.08528836 

0.08682834 

0.08837596 

16 

0.07961095 

0.08113994 

0.08268510 

0.08424482 

17 

0.07595263 

0.07748950 

0.07904332 

0.08001276 

18 

0.07270883 

0.07425402 

0.07581702 

0.07739660 

19 

0.06981408 

0.07136792 

0.07294045 

0.07453057 

20 

0.06721580 

0.06877875 

0.07036125 

0.07196211 

21 

0.06487186 

0.06644410 

0.06803674 

0.06964863 

22 

0.06274751 

0.06432926 

0.06593224 

0.06755533 

23 

0.06081399 

0.06240546 

0.06401896 

0.06565340 

24 

0.05904751 

0.06064881 

0.06227295 

0.06391891 

25 

0.05742796 

0.05903920 

0.06067418 

0.06233170 


110 





TABLE III 


Rate, 3% to 3%% 
Years, 26 to 50 


ANNUAL INSTALMENT 

The annuity which will amortize a capital of $1 at a fixed rate of compound 
interest for one to one hundred years. 


Years 

3% 

3%% 

3%% 

3%% 

26 

0.05593841 

0.05755970 

0.05920550 

0.06087473 

27 

0.05456429 

0.05619578 

0.05785250 

0.05953343 

28 

0.05329331 

0.05493502 

0.05660278 

0.05829543 

29 

0.05211476 

0.05376672 

0.05544553 

0.05714994 

30 

0.05101934 

0.05268164 

0.05437144 

0.05608763 

31 

0.04999900 

0.05167165 

0.05337249 

0.05510045 

32 

0.04904670 

0.05072968 

0.05244161 

0.05418131 

33 

0.04815619 

0.04984953 

0.05157254 

0.05332394 

34 

0.04732203 

0.04902574 

0.05075976 

0.05252286 

35 

0.04653934 

0.04825341 

0.04999843 

0.05177322 

36 

0.04580384 

0.04752823 

0.04928423 

0.05107062 

37 

0.04511166 

0.04684640 

0.04861330 

0.05041122 

38 

0.04445939 

0.04620439 

0.04798222 

0.04979158 

39 

0.04384390 

0.04559914 

0.04738780 

0.04920860 

40 

0.04326242 

0.04502786 

0.04^82736 

0.04865944 

41 

0.04271243 

0.04448808 

0.04629826 

0.04814164 

42 

0.04219171 

0.04397747 

0.04579833 

0.04765287 

43 

0.04169814 

0.04349396 

0.04532546 

0.04719104 

44 

0.04122990 

0.04303575 

0.04487770 

0.04675433 

45 

0.04078522 

0.04260104 

0.04445350 

0.04634100 

46 

0.04036256 

0.04218830 

0.04405113 

0.04594942 

47 

0.03996062 

0.04179614 

0.04366924 

0.04557823 

48 

0.03957780 

0.04142318 

0.04330650 

0.04522611 

49 

0.03921315 

0.04106824 

0.04296172 

0.04489178 

50 

0.03886552 

0.04073024 

0.04263375 

0.04457422 


Ill 





Rate, 3% to 3%X 
Years, 51 to 75 


TABLE III 


ANNUAL INSTALMENT 

The annuity which will amortize a capital of $1 at a fixed rate of compound 
interest for one to one hundred years. 


Years 

3% 

314^0 

31 / 2 % 

3%% 

51 

0.03853386 

0.04040813 

0.04232162 

0.04427235 

52 

0.03821722 

0.04010100 

0.04202433 

0.04398523 

53 

0.03791473 

0.03980794 

0.04174106 

0.04371200 

54 

0.03762561 

0.03952817 

0.04147095 

0.04345183 

55 

0.03734910 

0.03926091 

0.04121328 

0.04320398 

56 

0.03708449 

0.03900550 

0.04096735 

0.04296775 

57 

0.03683116 

0.03876128 

0.04073250 

0.04274250 

58 

0.03658851 

0.03852764 

0.04050814 

0.04252759 

59 

0.03635596 

0.03830403 

0.04029370 

0.04232251 

60 

0.03613300 

0.03808990 

0.04008866 

0.04212670 

61 

0.03591913 

0.03788479 

0.03989251 

0.04193967 

62 

0.03571384 

0.03768823 

0.03970485 

0.04176096 

63 

0.03551685 

0.03749980 

0.03952515 

0.04159013 

64 

0.03532762 

0.03731909 

0.03935311 

0.04142683 

65 

0.03514584 

0.03714571 

0.03918829 

0.04127063 

66 

0.03497112 

0.03697933 

0.03903035 

0.04112118 

67 

0.03480314 

0.03681960 

0.03887894 

0.04097814 

68 

0.03464160 

0.03666621 

0.03873380 

0.04084126 

69 

0.03448622 

0.03651884 

0.03859455 

0.04071014 

70 

0.03433665 

0.03637724 

0.03846099 

0.04058455 

71 

0.03419269 

0.03624116 

0.03833280 

0.04046425 

72 

0.03405407 

0.03611030 

0.03820976 

0.04034896 

73 

0.03392055 

0.03598450 

0.03809164 

0.04023846 

74 

0.03379194 

0.03586347 

0.03797819 

0.04013254 

75 

0.03366798 

0.03574700 

0.03786923 

0.04030098 


112 





TABLE III 


Ri»ts,3Xta 
.ycfiirs, 76t9..|P0 


ANNUAL INSTALMENT 


The annuity which will amortize a capital of $l at a fixed rate of compound 
interest for one to one hundred years. 


Years 3% 3^4% 3%% 3%%> 


76 

77 

78 

79 

80 


0.03354852 

0.03343333 

0.03332225 

0.03321512 

0.03311176 


0.03563493 

0.03552707 

0.03542320 

0.03532320 

0.03522686 


0.03776453 

0.03766393 

0.03756723 

0.03747427 

0.03738493 


0.03993354 

0.03984012 

0.03975046 

0.03966440 

0.03958182 


81 

82 

83 

84 

85 


0.03301202 

0.03291576 

0.03282286 

0.03273315 

0.03264652 


0.03513406 

0.03504467 

0.03495852 

0.03487548 

0.03479541 


0.03729897 

0.03721631 

0.03713678 

0.03706027 

0.03698664 


0.03950255 

0.03942645 

0.03935346 

0.03928321 

0.03921581 


86 

87 

88 

89 

90 


0.03256284 

0.03248203 

0.03240394 

0.03232849 

0.03225557 


0.03471822 

0.03464378 

0.03457199 

0.03450276 

0.03443598 


0.03691579 

0.03684758 

0.03678192 

0.03671870 

0.03665783 


0.03915106 

0.03908886 

0.03902911 

0.03897166 

0.03891644 


91 

92 

93 

94 

95 


0.03218509 

0.03211697 

0.03205107 

0.03198738 

0.03192579 


0.03437152 

0.03430934 

0.03424931 

0.03419139 

0.03413548 


0.03659920 

0.03654274 

0.03648834 

0.03643596 

0.03638548 


0.03886339 

0.03881238 

0.03876334 

0.03871621 

0.03867086 


96 

97 

98 

99 
100 


0.03186620 

0.03180858 

0.03175281 

0.03169887 

0.03164668 


0.03408149 

0.03402935 

0.03397903 

0.03393044 

0.03388349 


0.03633683 

0.03628997 

0.03624480 

0.03620124 

0.03615929 


0.03862728 

0.03858534 

0.03854503 

0.03850624 

0.03846895 


13 


113 




Rale, 4X to 4%% 
Years, 1 to 25 


TABLE III 

ANNUAL INSTALMENT 


The annuity which will amortize a capital of $1 at a fixed rate of compound 
interest for one to one hundred years. 


Years 

4% 

41 / 4 % 

4% 

4%<fo 

1 

1.0400000 

1.0425000 

1.0450000 

1.0475000 

2 

0.5301960 

0.5320977 

0.5339975 

0.5359017 

3 

0.3603485 

0.3620609 

0.3637736 

0.3654895 

4 

0.2754908 

0.2771148 

0.2787444 

0.2803763 

5 

0.2246279 

0.2262067 

0.2277923 

0.2294115 

6 

0.1907625 

0.1923172 

0.1938783 

0.1954451 

7 

0.1666103 

0.1681519 

0.1697014 

0.1712575 

8 

0.1485281 

0.1500647 

0.1516095 

0.1531621 

9 

0.1344934 

0.1360293 

0.1375745 

0.1391281 

10 

0.1232912 

0.1248299 

0.1263789 

0.1279372 

11 

0.1141493 

0.1156932 

0.1172483 

0.1188135 

12 

0.1065524 

0.1081033 

0.1096662 

0.1112403 

13 

0.1001439 

0.1017033 

0.1032753 

0.1048596 

14 

0.09466916 

0.09623792 

0.09782034 

0.09941574 

15 

0.08994124 

0.09152030 

0.09311378 

0.09472124 

16 

0.08582018 

0.08741010 

0.08901536 

0.09063544 

17 

0.08219868 

0.08380008 

0.08541758 

0.08705066 

18 

0.07899347 

0.08060672 

0.08223689 

0.08388354 

19 

0.07613870 

0.07776417 

0.07940734 

0.08106772 

20 

0.07358187 

0.07521974 

0.07687610 

0.07855055 

21 

0.07128021 

0.07293075 

0.07460056 

0.07628913 

22 

0.06919890 

0.07086230 

0.07254561 

0.07424852 

23 

0.06730914 

0.06898538 

0.07068246 

0.07239975 

24 

0.06558696 

0.06727622 

0.06898703 

0.07071873 

25 

0.06401204 

0.06571445 

0.06743900 

0.06918518 


114 




TABLE III 

ANNUAL INSTALMENT 


Rale, 4% to 4%% 
Years, 26 to SO 


The annuity which will amortize a capital of $1 at a fixed rate of compound 
interest for one to one hundred years. 


Years 

4% 

41 / 4^0 


4%% 

26 

0.06256747 

0.06428299 

0.06602133 

0.06778193 

27 

0.06123860 

0.06296731 

0.06471946 

0.06649445 

28 

0.06001304 

0.06175487 

0.06352080 

0.06531020 

29 

0.05888003 

0.06063493 

0.06241461 

0.06421833 

30 

0.05783015 

0.05959819 

0.06139154 

0.06320950 

31 

0.05685540 

0.05863647 

0.06044346 

0.06227554 

32 

0.05594869 

0.05774273 

0.05956318 

0.06140936 

33 

0.05510364 

0.05691060 

0.05874450 

0.06060457 

34 

0.05431482 

0.05613465 

0.05798190 

0.05985577 

35 

0.05357736 

0.05540991 

0.05727047 

0.05915797 

36 

0.05288694 

0.05473216 

0.05660577 

0.05850685 

37 

0.05223961 

0.05409741 

0.05598401 

0.05789845 

38 

0.05163200 

0.05350221 

0.05540168 

0.05732933 

39 

0.05106087 

0.05294347 

0.05485566 

0.05679640 

40 

0.05052353 

0.05241834 

0.05434315 

0.05629676 

41 

0.05001742 

0.05192436 

0.05386159 

0.05582795 

42 

0.04954025 

0.05145915 

0.05340867 

0.05538760 

43 

0.04908993 

0.05102067 

0.05298232 

0.05497365 

44 

0.04866460 

0.05060703 

0.05258071 

0.05458420 

45 

0.04826249 

0.05021653 

0.05220201 

0.05421754 

46 

0.04788209 

0.04984756 

0.05184470 

0.05387205 

47 

0.04752191 

0.04949869 

0.05150733 

0.05354634 

48 

0.04718070 

0.04916861 

0.05118857 

0.05323903 

49 

0.04685717 

0.04885608 

0.05088724 

0.05294894 

50 

0.04655022 

0.04856001 

0.05060214 

0.05267492 


115 





TABLE nr 

ANNUAL INSTALMENT 


lUte, 4% t6 
^eurs, 51 to 75 


The annuity which will amortize a capital of $1 at a fixed rate of compound 
interest for one to one hundred yeare. ' 


Years 

4fo 

' 41 / 4 % 

4V2fo 

4%fo 

51 

0.04625888 

0.04827936 

0.05033231 

0.05241595 

52 

0.04598214 

0.04801320 

0.05007679 

0.05217112 

53 

0.04571917 

0.04776062 

0.04983469 

0.05193950 

54 

0.04546913 

0.04752080 

0.04960517 

0.05172030 

55 

0.04523128 

0.04729303 

0.04938753 

0.05151278 

56 

0.04500490 

0.04707660 

0.04918107 

0.05131617 

57 

0.04478934 

0.04687082 

0.04898506 

0.05112994 

58 

0.04458404 

0.04667515 

0.04879898 

0.05095336 

59 

0.04438838 

0.04648895 

0.04862221 

0.05078593 

60 

0.04420188 

0.04631176 

0.04845426 

0.05062709 

61 

0.04402400 

0.04614306 

0.04829460 

0.05047642 

62 

0.04385432 

0.04598237 

0.04814283 

0.05033338 

63 

0.04369240 

0.04582927 

0.04799849 

0.05019761 

64 

0.04353781 

0.04568337 

0.04786114 

0.05006868 

65 

0.04339020 

0.04554431 

0.04773047 

0.04994621 

66 

0.04324923 

0.04541170 

0.04760608 

0.04982985 

67 

0.04311452 

0.04528521 

0.04748765 

0.04971926 

68 

0.04298580 

0.04516454 

0.04737484 

0.04961415 

69 

0.04286274 

0.04504940 

0.04726745 

0.04951419 

70 

0.04274508 

0.04493948 

0.04716512 

0.04941916 

71 

0.04263255 

0.04483456 

0.04706761 

0.04932882 

72 

0.04252492 

0.04473440 

0.04697465 

0.04924281 

73 

0.04242192 

0.04463872 

0.04688604 

0.04916105 

74 

0.04232335 

0.04454735 

0.04680156 

0.04908320 

75 

0.04222902 

0.04446002 

0.04672104 

0.04900913 


116 




Rute, 4% to 43 / 4 .^ 
Yw«, 76 to 100 


TABLE III 

ANNUAL JNSTALMENT 

The annuity which will amortize a capital of $1 at a fixed rate of compound 
interest for one to one hundred years. 


Years 

4% 

^ 41 / 4 % 

; 41/2^0 

4%% 

' 76 

0.04213869 

0.04437658 

0.04664421 

0.04893863 

77 

0.04205421 

0.04429685 

0.04657093 

0.04887150 

78 

0.04196941 

0.04422063 

0.04650104 

0.04880761 

79 

0.04189008 

0.04414777 

0.04643434 

0.04874672 

80 

0.04181410 

0.04407811 

0.04637070 

0.04868879 

81 

0.04174129 

0.04401149 

0.04630994 

0.04863361 

82 

0.04167152 

0.04394779 

0.04625197 

0.04858102 

83 

0.04160465 

0.04388683 

0.04619661 

0.04853096 

84 

0.04154055 

0.04382852 

0.04614379 

0.04848323 

85 

0.04147912 

0.04377274 

0.04609333 

0.04843777 

86 

0.04142020 

0.04371935 

0.04604515 

0.04839443 

87 

0.04136371 

0.04366828 

0.04599916 

0.04835317 

88 

0.04130954 

0.04361940 

0.04595520 

0.04831380 

89 

0.04125760 

0.04357261 

0.04591327 

0.04827629 

90 

0.04120776 

0.04352782 

0.04587314 

0.04824056 

91 

0.04115996 

0.04348497 

0.04583485 

0.04820647 

92 

0.04111411 

0.04344392 

0.04579827 

0.04817398 

93 

0.04107011 

0.04340461 

0.04576330 

0.04814300 

94 

0.04102790 

0.04336698 

0.04572989 

0.04811347 

95 

0.04098738 

0.04333093 

0.04569801 

0.04808531 

96 

0.04094850 

0.04329643 

0.04566748 

0.04805844 

97 

0.04091119 

0.04326338 

0.04563833 

0.04803284 

98 

0.04087538 

0.04323172 

0.04561045 

0.04800842 

99 

0.04084100 

0.04320140 

0.04558384 

0.04798513 

100 

0.04080802 

0.04317234 

0.04555836 

0.04796292 


117 





Rate, SX to S%X 
Years, 1 to 25 


TABLE III 

ANNUAL INSTALMENT 


The annuity which will amortize a capital of $1 at a fixed rate of compound 
interest for one to one hundred years. 


Years 

5% 


5%% 


1 

1.0500000 

1.0525000 

1.0550000 

1.0575000 

2 

0.5378048 

0.5397119 

0.5416180 

0.5435277 

3 

0.367208S 

0.3689309 

0.3706547 

0.3723804 

4 

0.2820121 

0.2836513 

0.2852951 

0.2869411 

5 

0.2309751 

0.2325733 

0.2341764 

0.2357840 

6 

0.1970177 

0.1985955 

0.2001788 

0.2017680 

7 

0.1728199 

0.1743889 

0.1759642 

0.1775463 

8 

0.1547219 

0.1562892 

0.1578639 

0.1594462 

9 

0.1406901 

0.1422606 

0.1438394 

0.1454265 

10 

0.1295047 

0.1310815 

0.1326677 

0.1342632 

11 

0.1203889 

0.1219747 

0.1235705 

0.1251766 

12 

0.1128254 

0.1144218 

0.1160291 

0.1176476 

13 

0.1064558 

0.1080639 

0.1096842 

0.1113162 

14 

0.1010240 

0.1026452 

0.1042790 

0.1059255 

15 

0.09634230 

0.09797717 

0.09962547 

0.1012874 

16 

0.09226992 

0.09391902 

0.09558242 

0.09725992 

17 

0.08869914 

0.09036300 

0.09204184 

0.09373570 

18 

0.08554620 

0.08722512 

0.08891978 

0.09063048 

19 

0.08274500 

0.08443922 

0.08615000 

0.08787730 

20 

0.08024255 

0.08195230 

0.08367926 

0.08542348 

21 

0.07799612 

0.07972144 

0.08146470 

0.08322582 

22 

0.07597052 

0.07771151 

0.07947119 

0.08124927 

23 

0.07413683 

0.07589354 

0.07766959 

0.07946470 

24 

0.07247088 

0.07424337 

0.07603533 

0.07784777 

25 

0.07095248 

0.07274068 

0.07454931 

0.07637812 


118 





TABLE III 

ANNUAL INSTALMENT 


Rate.5%toS%?jr 

Years, 26 to 50 


The annuity which will amortize a capital of $1 at a fixed rate of compound 
interest for one to one hundred years. 


Years 

5% 

5Vi<ro 

5y3% 

5%% 

26 

0.06956432 

0.07136820 

0.07319302 

0.07503857 

27 

0.06829186 

0.07011132 

0.07195225 

0.07381438 

28 

0.06712255 

0.06895745 

0.07081433 

0.07269290 

29 

0.06604555 

0.06789580 

0.06976853 

0.07166332 

30 

0.06505144 

0.06691693 

0.06880534 

0.07071622 

31 

0.06413211 

0.06601270 

0.06791661 

0.06984333 

32 

0.06328046 

0.06517596 

0.06709513 

0.06903750 

33 

0.06249007 

0.06440031 

0.06633465 

0.06829243 

34 

0.06175546 

0.06368030 

0.06562955 

0.06760250 

35 

0.06107173 

0.06301096 

0.06497486 

0.06696280 

36 

0.06043447 

0.06238793 

0.06436631 

0.06636891 

37 

0.05983980 

0.06180726 

0.06379988 

0.06581695 

38 

0.05928423 

0.06126548 

0.06327210 

0.06530333 

39 

0.05876563 

0.06075946 

0.06277988 

0.06482500 

40 

0.05827817 

0.06028637 

0.06232031 

0.06437906 

41 

0.05782230 

0.05984364 

0.06189087 

0.06396299 

42 

0.05739473 

0.05942900 

0.06148924 

0.06357443 

43 

0.05699333 

0.05904031 

0.06111334 

0.06321133 

44 

0.05661624 

0.05867569 

0.06076126 

0.06287179 

45 

0.05626174 

0.05833340 

0.06043124 

0.06255401 

46 

0.05592819 

0.05801188 

0.06012176 

0.06225649 

47 

0.05561421 

0.05770965 

0.05983127 

0.06197771 

48 

0.05531834 

0.05742544 

0.05955852 

0.06171639 

49 

0.05503965 

0.05715795 

0.05930228 

0.06147130 

50 

0.05477675 

0.05690609 

0.05906144 

0.06124130 


119 




Rate, SXtoS%% 
Year*,. 51 to 75 


TABLE III 


.ANNUAL INSTALMENT 

The annuity which will amortize a capital of $1 at a fixed rate of compound 
interest for one to one hundred years. 


Years 5% 5%^^ 5%% 


51 

52 

53 

54 

55 


0.05452868 

0.05429450 

0.05407333 

0.05386439 

0.05366686 


0.05666890 

0.05644533 

0.05623453 

0.05603568 

0.05584804 


0.05883493 

0.05862185 

0.05842127 

0.05823243 

0.05805454 


0.06102541 

0.06082263 

0.06063214 

0.06045308 

0.06028474 


56 

57 

58 

59 

60 


0.05348010 

0.05330344 

0.05313626 

0.05297802 

0.05282817 


0.05567095 

0.05550374 

0.05534577 

0.05519655 

0.05505549 


0.05788697 

0.05772898 

0.05758004 

0.05743955 

0.05730707 


0.06012641 

0.05997745 

0.05983725 

0.05970530 

0.05958103 


61 

62 

63 

64 

65 


0.05268627 

0.05255165 

0.05242441 

0.05230367 

0.05218914 


0.05492215 

0.05479604 

0.05467677 

0.05456392 

0.05445714 


0.05718204 

0.05706399 

0.05695257 

0.05684737 

0.05674799 


0.05946404 

0.05935380 

0.05924991 

0.05915205 

0.05905980 


66 

67 

68 

69 

70 


0.05208056 

0.05197760 

0.05187986 

0.05178715 

0.05169917 


0.05435605 

0.05426037 

0.05416975 

0.05408396 

0.05400267 


0.05665411 

0.05656544 

0.05648161 

0.05640240 

0.05632751 


0.05897281 

0.05889078 

0.05881343 

0.05874048 

0.05867165 


71 

72 

73 

74 

75 


0.05161564 

0.05153635 

0.05146104 

0.05138954 

0.05132162 


0.05392567 

0.05385274 

0.05378361 

0.05371810 

0.05365601 


0.05625674 

0.05618980 

0.05612650 

0.05606664 

0.05601000 


0.05860673 

0.05854544 

0.05848761 

0.05843305 

0.05838154 


120 





Rate,; 5% to 5%^ 
Years, 76 tO: 100 


TABLE 111 


♦ANNUAL INSTALMENT 


The annuity which will amortize a capital of $1 at a fixed rate of compound 
interest for one to one hundred years. 


Years 

5% 

5%% 

5V2^0 

76 

0.05125708 

0.05359715 

0.05595644 

77 

0.05119581 

0.05354134 

0.05590577 

78 

0.05113757 

0.05348841 

0.05585781 

79 

0.05108221 

0.05343822 

0.05581241 

80 

0.05102962 

0.05339064 

0.05576948 

81 

0.05097964 

0.05334550 

0.05572883 

82 

0.05093212 

0.05330267 

0.05569038 

83 

0.05088694 

0.05326205 

0.05565394 

84 

0.05084398 

0.05322351 

0.05561945 

85 

0.05080315 

0.05318695 

0.05558685 

86 

0.05076434 

0.05315227 

0.05555595 

87 

0.05072740 

0.05311932 

0.05552666 

88 

0.05069228 

0.05308809 

0.05549896 

89 

0.05065888 

0.05305844 

0.05547274 

90 

0.05062712 

0.05303031 

0.05544788 

91 

0.05059687 

0.05300362 

0.05542448 

92 

0.05056815 

0.05297826 

0.05540209 

93 

0.05054080 

0.05295418 

0.05538095 

94 

0.05051478 

0.05293134 

0.05536096 

95 

0.05049002 

0.05290967 

0.05534204 

96 

0.05046648 

0.05288907 

0.05532409 

97 

0.05044407 

0.05286953 

0.05530711 

98 

0.05042276 

0.05285098 

0.05529100 

99 

0.05040246 

0.05283336 

0.05527574 

100 

0.05038315 

0.05281666 

0.05526134 




0.05833290 

0.05828701 

0.05824364 

0.05820273 

0.05816411 

0.05812757 

0.05809309 

0.05806055 

0.05802975 

0.05800074 

0.05797327 

0.05794731 

0.05792284 

0.05789967 

0.05787780 

0.05785714 

0.05783761 

0.05781913 

0.05780169 

0.05778523 

0.05776964 

0.05775490 

0.05774098 

0.05772784 

0.05771540 


121 




Rate, 6X to 6%X 
Years, 1 to 25 


TABLE III 

ANNUAL INSTALMENT 


The annuity which will amortize a capital of $1 at a fixed rate of compound 
interest for one to one hundred years. 

/ 


Years 

6 % 

6y4% 


6 %% 

1 

1.0600000 

1.0625000 

1.0650000 

1.0675000 

2 

0.5454369 

0.5473496 

0.5492615 

0.5511769 

3 

0.3741098 

0.3758413 

0.3775766 

0.3793128 

4 

0.2885923 

0.2902456 

0.2919030 

0.2935640 

5 

0.2373967 

0.2390133 

0.2406348 

0.2422604 

6 

0.2033623 

0.2049628 

0.2065684 

0.2081795 

7 

0.1791347 

0.1807300 

0.1823315 

0.1839392 

8 

0.1610358 

0.1626329 

0.1642374 

0.1658488 

9 

0.1470221 

0.1486261 

0.1502380 

0.1518581 

10 

0.1358678 

0.1374820 

0.1391047 

0.1407366 

11 

0.1267929 

0.1284192 

0.1300554 

0.1317012 

12 

0.1192770 

0.1209174 

0.1225682 

0.1242297 

13 

0.1129600 

0.1146156 

0.1162826 

0.1179610 

14 

0.1075848 

0.1092566 

0.1109406 

0.1126366 

15 

0.1029627 

0.1046514 

0.1063528 

0.1080672 

16 

0.09895205 

0.1006580 

0.1023776 

0.1041108 

17 

0.09544467 

0.09716839 

0.09890632 

0.1006587 

18 

0.09235646 

0.09409802 

0.09585460 

0.09762619 

19 

0.08962076 

0.09138046 

0.09315579 

0.09494669 

20 

0.08718450 

0.08896232 

0.09075642 

0.09256668 

21 

0.08500449 

0.08680054 

0.08861328 

0.09044292 

22 

0.08304552 

0.08485966 

0.08669120 

0.08883998 

23 

0.08127843 

0.08311066 

0.08496084 

0.08682862 

24 

0.07967997 

0.08152914 

0.08339772 

0.08528444 

25 

0.07822667 

0.08009470 

0.08198148 

0.08388690 


122 




TABLE III 


Rate, 6% to 6%%’ 
Years, 26 to 50 


ANNUAL INSTALMENT 

The annuity which will amortize a capital of $1 at a fixed rate of compound 
interest for one to one hundred years. 


Years 

6 % 

6 %% 


6 %% 

26 

0.07690432 

0.07878992 

0.08069480 

0.08261862 

27 

0.07569712 

0.07760022 

0.07952287 

0.08146487 

28 

0.07459252 

0.07651280 

0.07845304 

0.08041292 

29 

0.07357957 

0.07551683 

0.07747440 

0.07945186 

30 

0.07264889 

0.07460289 

0.07657745 

0.07857214 

31 

0.07179218 

0.07376265 

0.07575395 

0.07776554 

32 

0.07100228 

0.07298897 

0.07499665 

0.07702485 

33 

0.07027292 

0.07227547 

0.07429923 

0.07634365 

34 

0.06959840 

0.07161653 

0.07365612 

0.07571640 

35 

0.06897383 

0.07100732 

0.07306225 

0.07513809 

36 

0.06839482 

0.07044326 

0.07251332 

0.07460427 

37 

0.06785739 

0.06992053 

0.07200535 

0.07411105 

38 

0.06735810 

0.06943558 

0.07153480 

0.07365492 

39 

0.06689375 

0.06898528 

0.07109852 

0.07323268 

40 

0.06646150 

0.06856680 

0.07069373 

0.07284150 

41 

0.06605883 

0.06817748 

0.07031782 

0.07247883 

42 

0.06568340 

0.06781513 

0.06996843 

0.07214235 

43 

0.06533310 

0.06747756 

0.06964352 

0.07182996 

44 

0.06500606 

0.06716293 

0.06934118 

0.07153982 

45 

0.06470047 

0.06686946 

0.06905966 

0.07127006 

46 

0.06441483 

0.06659570 

0.06879743 

0.07101926 

47 

0.06414767 

0.06633985 

0.06855300 

0.07078593 

48 

0.06389763 

0.06610098 

0.06832506 

0.07056868 

49 

0.06366353 

0.06587770 

0.06811238 

0.07036642 

50 

0.06344426 

0.06566895 

0.06791393 

0.07017795 


123 





Rat#,,6i?jr to,6?4% 

Ye«r«.S 51 to 75 


TABLE III 


ANNUAL INSTALMENT 


The annuity which will amortize a capital of $1 at a fixed rate of compound 
interest for one to one hundred years. 


Years 6% 6%% 6^4% 6%% 


51 

52 

53 

54 

55 


0.06323876 

0.06304614 

0.06286550 

0.06269603 

0.06253696 


0.06547367 

0.06529095 

0.06511987 

0.06495970 

0.06480969 


0.06772862 

0.06755555 

0.06739383 

0.06724268 

0.06710136 


0.07000233 

0.06983865 

0.06968598 

0.06954355 

0.06941066 


56 

57 

58 

59 

60 


0.06238763 

0.06224743 

0.06211571 

0.06199200 

0.06187570 


0.06466909 

0.06453734 

0.06441383 

0.06429800 

0.06418939 


0.06696923 

0.06684543 

0.06673002 

0.06662176 

0.06652048 


0.06928663 

0.06917088 

0.06906278 

0.06896182 

0.06886750 


61 

62 

63 

64 

65 


0.06176643 

0.06166366 

0.06156704 

0.06147614 

0.06139064 


0.06407771 

0.06399187 

0.06390214 

0.06381793 

0.06373887 


0.06642563 

0.06633685 

0.06625366 

0.06617578 

0.06610280 


0.06877942 

0.06869706 

0.06862015 

0.06854820 

0.06848095 


66 

67 

68 

69 

70 


0.06131021 

0.06123450 

0.06116284 

0.06109624 

0.06103311 


0.06366464 

0.06359493 

0.06352947 

0.06346799 

0.06341020 


0.06603443 

0.06597035 

0.06591029 

0.06585402 

0.06580123 


0.06841808 

0.06835930 

0.06830432 

0.06825289 

0.06820476 


71 0.06097368 0.06335593 

72 0.06091774 0.06330494 

73 0.06086504 0.06325701 

74 0.06081540 0.06321199 

75 0.06076867 0.06316964 


0.06575178 

0.06570542 

0.06566190 

0.06562113 

0.06558286 


0.06815983 

0.06811766 

0.06807835 

0.06804145 

0.06800695 


124 




TABLE III 


Rate, 6^ to 6%% 
Year* 76 to 100 


ANNUAL INSTALMENT 


The annuity which will amortize a capital of $1 at a fixed rate of compound 
interest for one to one hundred years. 


Years 

6 % 

6y4% 

6y2% 

6 %% 

76 

0.06072463 

0.06312984 

0.06554700 

0.06797470 

77 

0.06068316 

0.06309246 

0.06551336 

0.06794448 

78 

0.06064407 

0.06305734 

0.06548180 

0.06791619 

79 

0.06060726 

0.06302427 

0.06545216 

0.06788972 

80 

0.06057253 

0.06299314 

0.06542440 

0.06786490 

81 

0.06053984 

0.06296391 

0.06539833 

0.06784172 

82 

0.06050903 

0.06293646 

0.06537390 

0.06781995 

83 

0.06047997 

0.06291060 

0.06535093 

0.06779966 

84 

0.06045260 

0.06288631 

0.06532939 

0.06778065 

85 

0.06042681 

0.06286344 

0.06530924 

0.06776285 

86 

0.06040250 

0.06284197 

0.06529024 

0.06774613 

87 

0.06037955 

0.06282174 

0.06527247 

0.06773053 

88 

0.06035793 

0.06280273 

0.06525579 

0.06771589 

89 

0.06033758 

0.06278483 

0.06524010 

0.06770220 

90 

0.06031838 

0.06276800 

0.06522537 

0.06768939 

91 

0.06030027 

0.06275216 

0.06521159 

0.06767739 

92 

0.06028317 

0.06273727 

0.06519865 

0.06766615 

93 

0.06026706 

0.06272326 

0.06518647 

0.06765560 

94 

0.06025188 

0.06271007 

0.06517507 

0.06764578 

95 

0.06023756 

0.06269770 

0.06516437 

0.06763650 

96 

0.06022408 

0.06268601 

0.06515430 

0.06762786 

97 

0.06021134 

0.06267504 

0.06514486 

0.06761975 

98 

0.06019929 

0.06266473 

0.06513600 

0.06761216 

99 

0.06018801 

0.06265501 

0.06512768 

0.06760506 

100 

0.06017736 

0.06264590 

0.06511986 

0.06759843 


125 




Rate, 7% to 7%% 
Years. 1 to 25 


TABLE III 

ANNUAL INSTALMENT 


The annuity which will amortize a capital of $1 at a fixed rate of compound 
interest for one to one hundred years. 


Years 

7% 

7%fo 

7V2^0 

7%% 

1 

1.0700000 

1.0725000 

1.0750000 

1.0775000 

2 

0.5530918 

0.5550099 

0.5569276 

0.5588484 

3 

0.3810513 

0.3827945 

0.3845387 

0.3862847 

4 

0.2952281 

0.2968963 

0.2985675 

0.3002428 

5 

0.2438910 

0.2455255 

0.2471649 

0.2488083 

6 

0.2097959 

0.2114178 

0.2130447 

0.2146774 

7 

0.1855533 

0.1871736 

0.1888001 

0.1904330 

8 

0.1674677 

0.1690940 

0.1707269 

0.1723673 

9 

0.1534864 

0.1551229 

0.1567670 

0.1584194 

10 

0.1423775 

0.1440273 

0.1456858 

0.1473533 

11 

0.1333568 

0.1350223 

0.1366974 

0.1383821 

12 

0.1259019 

0.1275847 

0.1292778 

0.1309812 

13 

0.1196508 

0.1213519 

0.1230641 

0.1247874 

14 

0.1143449 

0.1160652 

0.1177973 

0.1195412 

15 

0.1097946 

0.1115345 

0.1132872 

0.1150522 

16 

0.1058576 

0.1076177 

0.1093911 

0.1111776 

17 

0.1024252 

0.1042056 

0.1060000 

0.1078080 

18 

0.09941254 

0.1012135 

0.1030289 

0.1048585 

19 

0.09675297 

0.09857444 

0.1004108 

0.1022620 

20 

0.09439290 

0.09623482 

0.09809214 

0.09996470 

21 

0.09228898 

0.09415124 

0.09602932 

0.09792314 

22 

0.09040572 

0.09228814 

0.09418680 

0.09610160 

23 

0.08871386 

0.09061622 

0.09253526 

0.09447066 

24 

0.08718896 

0.08911102 

0.09105002 

0.09300582 

25 

0.08581049 

0.08775188 

0.08971062 

0.09168640 


126 




TABLE III 


Rate, 1% to 7%% 
Years, 26 to 56 


ANNUAL INSTALMENT 


The annuity which will amortize a capital of $1 at a fixed rate of compound 
interest for one to one hundred years. 


Years 

7% 

7%fo 

71 / 2 % 

7%% 

26 

0.08456100 

0.08652150 

0.08849954 

0.09049492 

27 

0.08342572 

0.08540492 

0.08740200 

0.08941654 

28 

0.08239192 

0.08438950 

0.08640516 

0.08843846 

29 

0.08144864 

0.08346424 

0.08549805 

0.08754970 

30 

0.08058639 

0.08261960 

0.08467122 

0.08674068 

31 

0.07979689 

0.08184732 

0.08391626 

0.08600312 

32 

0.07907290 

0.08114016 

0.08322596 

0.08532974 

33 

0.07840803 

0.08049169 

0.08259394 

0.08471414 

34 

0.07779674 

0.07989635 

0.08201458 

0.08415078 

35 

0.07723395 

0.07934916 

0.08148289 

0.08363450 

36 

0.07671530 

0.07884564 

0.08099446 

0.08316110 

37 

0.07623682 

0.07838190 

0.08054534 

0.08272642 

38 

0.07579504 

0.07795424 

0.08013194 

0.08232712 

39 

0.07538692 

0.07755980 

0.07975122 

0.08195994 

40 

0.07500912 

0.07719567 

0.07940032 

0.08162210 

41 

0.07465962 

0.07685917 

0.07907664 

0.08131106 

42 

0.07433589 

0.07654809 

0.07877785 

0.08102446 

43 

0.07403589 

0.07626023 

0.07850202 

0.08076030 

44 

0.07375770 

0.07599380 

0.07824707 

0.08051667 

45 

0.07349960 

0.07574703 

0.07801147 

0.08029186 

46 

0.07325999 

0.07551842 

0.07779352 

0.08008434 

47 

0.07303742 

0.07530647 

0.07759194 

0.07989276 

48 

0.07283058 

0.07510989 

0.07740527 

0.07971570 

49 

0.07263853 

0.07492757 

0.07723247 

0.07955212 

50 

0.07245987 

0.07475835 

0.07707242 

0.07940090 


127 




Rale, 1% to rik% 
Years, 51 lo 75 


TABLE III 


ANNUAL INSTALMENT 

The annuity which will amortize a capital of $1 at a fixed rate of compound 
interest for one to one hundred years. 


Years 7% 7%% 


51 

52 

53 

54 

55 


0.07229365 

0.07213902 

0.07199507 

0.07186110 

0.07173630 


0.07460127 

0.07445540 

0.07431990 

0.07419400 

0.07407698 


0.07692414 

0.07678669 

0.07665930 

0.07654112 

0.07643154 


0.07926107 

0.07913176 

0.07901207 

0.07890135 

0.07879889 


56 

57 

58 

59 

60 


0.07162012 

0.07151182 

0.07141093 

0.07131688 

0.07122923 


0.07396822 

0.07386709 

0.07377305 

0.07368557 

0.07360422 


0.07632990 

0.07623557 

0.07614804 

0.07606680 

0.07599140 


0.07870400 

0.07861615 

0.07853482 

0.07845944 

0.07838964 


61 

62 

63 

64 

65 


0.07114748 

0.07107126 

0.07100017 

0.07093388 

0.07087203 


0.07352850 

0.07345807 

0.07339248 

0.07333148 

0.07327468 


0.07592140 

0.07585640 

0.07579599 

0.07573992 

0.07568782 


0.07832497 

0.07826505 

0.07820952 

0.07815807 

0.07811037 


66 

67 

68 

69 

70 


0.07081432 

0.07076045 

0.07071022 

0.07066332 

0.07061952 


0.07322182 

0.07317257 

0.07312672 

0.07308402 

0.07304420 


0.07563942 

0.07559447 

0.07555272 

0.07551387 

0.07547782 


0.07806614 

0.07802510 

0.07798712 

0.07795192 

0.07791924 


71 

72 

73 

74 

75 


0.07057867 

0.07054050 

0.07050490 

0.07047167 

0.07044058 


0.07300715 

0.07297263 

0.07294048 

0.07291057 

0.07288268 


0.07544425 

0.07541305 

0.07538414 

0.07535720 

0.07533215 


0.07788892 

0.07786080 

0.07783474 

0.07781057 

0.07778814 


128 




TABLE III 

ANNUAL INSTALMENT 


Rate, 1% to 7%% 
Years, 76 to 100 


The annuity which will amortize a capital of $1 at a fixed rate of compound 
interest for one to one hundred years. 


Years 

7% 

7%% 

71 / 2 % 

7%% 

76 

0.07041160 

0.07285665 

0.07530892 

0.07776735 

77 

0.07038455 

0.07283245 

0.07528725 

0.07774807 

78 

0.07035925 

0.07280990 

0.07526715 

0.07773014 

79 

0.07033563 

0.07278882 

0.07524847 

0.07771357 

80 

0.07031347 

0.07276925 

0.07523110 

0.07769817 

81 

0.07029298 

0.07275095 

0.07521490 

0.07768385 

82 

0.07027373 

0.07273393 

0.07519985 

0.07767062 

83 

0.07025578 

0.07271808 

0.07518589 

0.07765834 

84 

0.07023898 

0.07270330 

0.07517287 

0.07764694 

85 

0.07022330 

0.07268952 

0.07516079 

0.07763632 

86 

0.07020865 

0.07267668 

0.07514957 

0.07762652 

87 

0.07019495 

0.07266470 

0.07513910 

0.07761740 

88 

0.07018215 

0.07265353 

0.07512938 

0.07760894 

89 

0.07017021 

0.07264313 

0.07512031 

0.07760109 

90 

0.07015905 

0.07263343 

0.07511191 

0.07759382 

91 

0.07014862 

0.07262438 

0.07510409 

0.07758707 

92 

0.07013885 

0.07261598 

0.07509685 

0.07758079 

93 

0.07012978 

0.07260812 

0.07509005 

0.07757497 

94 

0.07012126 

0.07260082 

0.07508375 

0.07756959 

95 

0.07011333 

0.07259400 

0.07507793 

0.07756457 

96 

0.07010592 

0.07258763 

0.07507250 

0.07755994 

97 

0.07009896 

0.07258170 

0.07506743 

0.07755562 

98 

0.07009248 

0.07257618 

0.07506272 

0.07755160 

99 

0.07008640 

0.07257102 

0.07505833 

0.07754787 

100 

0.07008076 

0.07256618 

0.07505427 

0.07754445 


14 

129 






Rate, 8% to 8%X 
Years, 1 to 25 


TABLE III 


ANNUAL INSTALMENT 

at a fixed rate of compound 


The annuity which will amortize a capital of 
interest for one to one hundred years. 


Y^ears 

8<fo 

81/4% 

8 %% 

8 %% 

1 

1.0800000 

1.0825000 

1.0850000 

1.0875000 

2 

0.5607692 

0.5626929 

0.5646162 

0.5665425 

3 

0.3880333 

0.3897854 

0.3915395 

0.3932954 

4 

0.3019208 

0.3036024 

0.3052883 

0.3069765 

5 

0.2504566 

0.2521089 

0.2537661 

0.2554270 

6 

0.2163152 

0.2179587 

0.2196074 

0.2212608 

7 

0.1920723 

0.1937178 

0.1953694 

0.1970266 

8 

0.1740147 

0.1756691 

0.1773309 

0.1789990 

9 

0.1600796 

0.1617479 

0.1634239 

0.1651073 

10 

0.1490294 

0.1507142 

0.1524078 

0.1541096 

11 

0.1490763 

0.1417799 

0.1434930 

0.1452151 

12 

0.1326949 

0.1344189 

0.1361530 

0.1378968 

13 

0.1265217 

0.1282669 

0.1300229 

0.1317894 

14 

0.1212967 

0.1230639 

0.1248426 

0.1266322 

15 

0.1168295 

0.1186190 

0.1204205 

0.1222338 

16 

0.1129768 

0.1147889 

0.1166136 

0.1184505 

17 

0.1096294 

0.1114642 

0.1133120 

0.1151727 

18 

0.1067021 

0.1185595 

0.1104305 

0.1123147 

19 

0.1041276 

0.1060075 

0.1079014 

0.1098091 

20 

0.1018522 

0.1037544 

0.1056710 

0.1076017 

21 

0.09983219 

0.1017564 

0.1036954 

0.1056489 

22 

0.09803200 

0.09997795 

0.1019382 

0.1039147 

23 

0.09642214 

0.09838937 

0.1003720 

0.1023695 

24 

0.09497794 

0.09696604 

0.09896974 

0.1009887 

25 

0.09367872 

0.09568732 

0.09771172 

0.09975145 


130 





TABLE III 


Rate, 8% to S%% 
Years, 26 to 50 


ANNUAL INSTALMENT 


The annuity which will amortize a capital of $1 at a fixed rate of compound 
interest for one to one hundred years. 


Years 

8% 

81/4^0 

8V2^0 

00 

26 

0.09250709 

0.09453564 

0.09658020 

0.09864019 

27 

0.09144806 

0.09349612 

0.09556024 

0.09764000 

28 

0.09048891 

0.09255594 

0.09463920 

0.09673807 

29 

0.08961856 

0.09170404 

0.09380580 

0.09592312 

30 

0.08882742 

0.09093086 

0.09305060 

0.09518592 

31 

0.08810726 

0.09022812 

0.09236530 

0.09451782 

32 

0.08745080 

0.08958856 

0.09174252 

0.09391182 

33 

0.08685158 

0.08900572 

0.09117586 

0.09336140 

34 

0.08630414 

0.08847398 

0.09065984 

0.09286086 

35 

0.08580322 

0.08798844 

0.09018938 

0.09240540 

36 

0.08534460 

0.08754456 

0.08976006 

0.09199048 

37 

0.08492440 

0.08713848 

0.08936804 

0.09161212 

38 

0.08453870 

0.08676668 

0.08900968 

0.09126704 

39 

0.08418510 

0.08642604 

0.08868190 

0.09095198 

40 

0.08386018 

0.08611370 

0.08838204 

0.09066416 

41 

0.08356146 

0.08582718 

0.08810740 

0.09040118 

42 

0.08328680 

0.08556420 

0.08785578 

0.09016062 

43 

0.08303412 

0.08532268 

0.08762510 

0.08994060 

44 

0.08280150 

0.08510076 

0.08741364 

0.08973920 

45 

0.08258728 

0.08489680 

0.08721958 

0.08955482 

46 

0.08238989 

0.08470924 

0.08704152 

0.08938592 

47 

0.08220796 

0.08453670 

0.08687808 

0.08923116 

48 

0.08204026 

0.08437796 

0.08672798 

0.08908934 

49 

0.08188554 

0.08423182 

0.08659004 

0.08895934 

50 

0.08174284 

0.08409730 

0.08646330 

0.08884012 


131 





Rate, 8X to 8%% 
Years, 51 to 75 


TABLE III 


ANNUAL INSTALMENT 

The annuity which will amortize a capital of $1 at a fixed rate of compound 
interest for one to one hundred years. 


Years 

00 


8 %% 

8 %% 

51 

0.08161116 

0.08397338 

0.08634688 

0.08873080 

52 

0.08148958 

0.08385924 

0.08624004 

0.08863048 

53 

0.08137736 

0.08375406 

0.08614140 

0.08853844 

54 

0.08127370 

0.08365714 

0.08605088 

0.08845398 

55 

0.08117794 

0.08356780 

0.08596762 

0.08837648 

56 

0.08108952 

0.08348544 

0.08589102 

0.08830528 

57 

0.08100780 

0.08340954 

0.08582054 

0.08823996 

58 

0.08093226 

0.08333948 

0.08575580 

0.08817992 

59 

0.08086248 

0.08327492 

0.08569596 

0.08812482 

60 

0.08079792 

0.08321540 

0.08564104 

0.08807422 

61 

0.08073827 

0.08316044 

0.08559048 

0.08802778 

62 

0.08068316 

0.08310972 

0.08554390 

0.08798508 

63 

0.08063214 

0.08306288 

0.08550108 

0.08794584 

64 

0.08058496 

0.08301972 

0.08546160 

0.08790976 

65 

0.08054132 

0.08297988 

0.08542526 

0.08787668 

66 

0.08050096 

0.08294308 

0.08539180 

0.08784624 

67 

0.08046367 

0.08290914 

0.08536098 

0.08781826 

68 

0.08042916 

0.08287784 

0.08533262 

0.08779256 

69 

0.08039719 

0.08284889 

0.08530644 

0.08776894 

70 

0.08036764 

0.08282220 

0.08528234 

0.08774724 

71 

0.08034032 

0.08279754 

0.08526018 

0.08772732 

72 

0.08031497 

0.08277482 

0.08523974 

0.08770900 

73 

0.08029157 

0.08275382 

0.08522090 

0.08769212 

74 

0.08026987 

0.08273442 

0.08520354 

0.08767664 

75 

0.08024986 

0.08271649 

0.08518756 

0.08766240 


132 





TABLE III 

ANNUAL INSTALMENT 


Rale, 8% to 8%% 
Year*, 76 to 100 


The annuity which will amortize a capital of $1 at a fixed rate of compound 
interest for one to one hundred years. 


Years 

00 

81/4% 


8 %% 

76 

0.08023126 

0.08269996 

0.08517286 

0.08764930 

77 

0.08021410 

0.08268468 

0.08515928 

0.08763726 

78 

0.08019820 

0.08267058 

0.08514672 

0.08762620 

79 

0.08018347 

0.08265752 

0.08513528 

0.08761604 

80 

0.08016986 

0.08264550 

0.08512464 

0.08760670 

81 

0.08015724 

0.08263440 

0.08511486 

0.08759812 

82 

0.08014557 

0.08262414 

0.08510586 

0.08759022 

83 

0.08013480 

0.08261466 

0.08509754 

0.08758296 

84 

0.08012482 

0.08260592 

0.08508992 

0.08757628 

85 

0.08011550 

0.08259784 

0.08508286 

0.08757014 

86 

0.08012540 

0.08259036 

0.08507635 

0.08756450 

87 

0.08009902 

0.08258346 

0.08507032 

0.08755928 

88 

0.08009169 

0.08257710 

0.08506482 

0.08755452 

89 

0.08008487 

0.08257120 

0.08505977 

0.08755012 

90 

0.08007862 

0.08256580 

0.08505507 

0.08754608 

91 

0.08007275 

0.08256080 

0.08505076 

0.08754232 

92 

0.08006737 

0.08255616 

0.08504682 

0.08753898 

93 

0.08006240 

0.08255188 

0.08504312 

0.08753582 

94 

0.08005774 

0.08254786 

0.08503972 

0.08753292 

95 

0.08005344 

0.08254420 

0.08503662 

0.08753030 

96 

0.08004950 

0.08254080 

0.08503364 

0.08752784 

97 

0.08004582 

0.08253772 

0.08503112 

0.08752560 

98 

0.08004244 

0.08253488 

0.08502866 

0.08752352 

99 

0.08003930 

0.08253220 

0.08502642 

0.08752164 

100 

0.08003636 

0.08252978 

0.08502440 

0.08751990 


133 




Rate.9%to9%% 
Years, 1 to 25 


TABLE III 


ANNUAL INSTALMENT 


The annuity which will amortize a capital of $1 at a fixed rate of compound 
interest for one to one hundred years. 


Years 

9% 


9%% 

9%% 

1 

1.0900000 

1.0925000 

1.0950000 

1.0975000 

2 

0.5684689 

0.5703978 

0.5723271 

0.5742584 

3 

0.3950547 

0.3968162 

0.3985802 

0.4003467 

4 

0.3086690 

0.3103644 

0.3120629 

0.3137653 

5 

0.2570928 

0.2587625 

0.2604366 

0.2621150 

6 

0.2229200 

0.2245842 

0.2262534 

0.2279280 

7 

0.1986905 

0.2003603 

0.2020361 

0.2037179 

8 

0.1806745 

0.1823566 

0.1840457 

0.1857419 

9 

0.1667988 

0.1684979 

0.1702045 

0.1719188 

, 10 

0.1558201 

0.1575391 

0.1592662 

0.1610017 

11 

0.1469467 

0.1486874 

0.1504369 

0.1521956 

12 

0.1396607 

0.1414144 

0.1431877 

0.1449708 

13 

0.1335666 

0.1353541 

0.1371520 

0.1389602 

14 

0.1284332 

0.1302452 

0.1320682 

0.1339018 

15 

0.1240589 

0.1258956 

0.1277437 

0.1296032 

16 

0.1202999 

0.1221614 

0.1240347 

0.1259198 

! 17 

0.1170463 

0.1189324 

0.1208308 

0.1227415 

18 

0.1142124 

0.1161228 

0.1180461 

0.1199820 

19 

0.1117304 

0.1136651 

0.1156128 

0.1175735 

20 

0.1095465 

0.1115049 

0.1134767 

0.1154617 

21 

0.1076166 

0.1095983 

0.1115937 

0.1136025 

22 

0.1059050 

0.1079095 

0.1099278 

0.1119598 

23 

0.1043819 

0.1064086 

0.1084494 

0.1105039 

24 

0.1030226 

0.1050709 

0.1071335 

0.1092099 

25 

0.1018062 

0.1038757 

134 

0.1059594 

0.1080572 





TABLE III 

ANNUAL INSTALMENT 


Rate,9%to9%% 
Years, 26 to 50 


The annuity which will amortize a capital of $1 at a fixed rate of compound 
interest for one to one hundred years. 


Years 

9% 

m<^o 

9%% 

9%% 

26 

0.1007153 

0.1028052 

0.1049093 

0.1070275 

27 

0.09973490 

0.1018446 

0.1039689 

0.1061063 

28 

0.09885210 

0.1009808 

0.1031239 

0.1052807 

29 

0.09805570 

0.1002030 

0.1023644 

0.1045396 

30 

0.09733632 

0.09950139 

0.1016806 

0.1038735 

31 

0.09668557 

0.09886780 

0.1010640 

0.1032736 

32 

0.09609622 

0.09829482 

0.1005073 

0.1027331 

33 

0.09556174 

0.09777620 

0.1000044 

0.1022456 

34 

0.09507659 

0.09730629 

0.09954932 

0.1018054 

35 

0.09463582 

0.09688009 

0.09913754 

0.1014075 

36 

0.09423506 

0.09649320 

0.09876439 

0.1010478 

37 

0.09387032 

0.09614184 

0.09842602 

0.1007223 

38 

0.09353816 

0.09582240 

0.09811902 

0.1004274 

39 

0.09323552 

0.09553184 

0.09784034 

0.1001602 

40 

0.09295962 

0.09526749 

0.09758719 

0.09991800 

41 

0.09270790 

0.09502677 

0.09735717 

0.09969835 

42 

0.09247814 

0.09480746 

0.09714802 

0.09949905 

43 

0.09226839 

0.09460764 

0.09695782 

0.09931815 

44 

0.09207674 

0.09442546 

0.09678477 

0.09915389 

45 

0.09190164 

0.09425936 

0.09662727 

0.09900469 

46 

0.09174156 

0.09410780 

0.09648389 

0.09886912 

47 

0.09159526 

0.09396952 

0.09635332 

0.09874594 

48 

0.09146140 

0.09384329 

0.09623437 

0.09863397 

49 

0.09133892 

0.09372802 

0.09612602 

0.09853215 

50 

0.09122686 

0.09362280 

0.09602729 

0.09843957 


135 




Rate, 9% to 9%% 
Years, 51 to 75 


TABLE III 


ANNUAL INSTALMENT 


The annuity which will amortize a capital of $1 at a fixed rate of compound 
interest for one to one hundred years. 


Years 

9^0 

m^o 

9%% 

9%fo 

51 

0.09112429 

0.09352670 

0.09593729 

0.09835534 

52 

0.09103042 

0.09343886 

0.09585517 

0.09827872 

53 

0.09094442 

0.09335866 

0.09578040 

0.09820897 

54 

0.09086568 

0.09328530 

0.09571222 

0.09814567 

55 

0.09079360 

0.09321832 

0.09564997 

0.09808784 

56 

0.09072754 

0.09315706 

0.09559330 

0.09803539 

57 

0.09066706 

0.09310108 

0.09554150 

0.09798760 

58 

0.09061158 

0-09304994 

0.09549429 

0.09794409 

59 

0.09056074 

0.09300309 

0.09545114 

0.09790444 

60 

0.09051420 

0.09296030 

0.09541182 

0.09786840 

61 

0.09047152 

0.09292112 

0.09537600 

0.09783554 

62 

0.09043238 

0.09288532 

0.09534329 

0.09780567 

63 

0.09039654 

0.09285256 

0.09531340 

0.09777842 

64 

0.09036368 

0.09282260 

0.09528610 

0.09775360 

65 

0.09033352 

0.09279520 

0.09526122 

0.09773102 

66 

0.09030590 

0.09277012 

0.09523850 

0.09771044 

67 

0.09028056 

0.09274716 

0.09521774 

0.09769172 

68 

0.09025736 

0.09272622 

0.09519880 

0.09767465 

69 

0.09023606 

0.09270702 

0.09518154 

0.09765912 

70 

0.09021648 

0.09268944 

0.09516577 

0.09764492 

71 

0.09019856 

0.09267336 

0.09515137 

0.09763205 

72 

0.09018214 

0.09265868 

0.09513820 

0.09762027 

73 

0.09016704 

0.09264522 

0.09512622 

0.09760957 

74 

0.09015326 

0.09263292 

0.09511524 

0.09759982 

75 

0.09014056 

0.09262164 

0.09510527 

0.09759097 


136 




TABLE III 

ANNUAL INSTALMENT 


Rate, 9%to9%X 
Years, 76 to 100 


The annuity which will amortize a capital of $1 at a fixed rate of compound 
interest for one to one hundred years. 


Years 9% 9%% 9%^^ 


76 

77 

78 

79 

80 

81 

82 

83 

84 

85 

86 

87 

88 

89 

90 

91 

92 

93 

94 

95 

96 

97 

98 

99 
100 


0.09012894 

0.09011832 

0.09010850 

0.09009954 

0.09009132 

0.09008368 

0.09007686 

0.09007046 

0.09006478 

0.09005938 

0.09005444 

0.09004990 

0.09004580 

0.09004198 

0.09003852 

0.09003534 

0.09003244 

0.09002976 

0.09002732 

0.09002504 

0.09002300 

0.09002108 

0.09001934 

0.09001774 

0.09001630 


0.09261132 

0.09260186 

0.09259322 

0.09258538 

0.09257816 

0.09257154 

0.09256544 

0.09255996 

0.09255486 

0.09255022 

0.09254594 

0.09254204 

0.09253850 

0.09253524 

0.09253226 

0.09252950 

0.09252700 

0.09252472 

0.09252264 

0.09252070 

0.09251898 

0.09251736 

0.09251592 

0.09251452 

0.09251330 


0.09509610 

0.09508779 

0.09508019 

0.09507314 

0.09506684 

0.09506104 

0.09505572 

0.09505082 

0.09504652 

0.09504242 

0.09503874 

0.09503537 

0.09503230 

0.09502949 

0.09502692 

0.09502459 

0.09502246 

0.09502052 

0.09501872 

0.09501710 

0.09501564 

0.09501429 

0.09501302 

0.09501192 

0.09501086 


0.09758290 

0.09757547 

0.09756880 

0.09756269 

0.09755709 

0.097552C0 

0.09754737 

0.09754317 

0.09753932 

0.09753589 

0.09753264 

0.09752974 

0.09752710 

0.09752467 

0.09752247 

0.09752047 

0.09751867 

0.09751697 

0.09751547 

0.09751410 

0.09751284 

0.09751180 

0.09751074 

0.09750967 

0.09750882 





TABLE IV 


SEMI-ANNUITY FOR INSTALMENT 

q ’*—1 

The semi-annuity, or semi-annual instalment, paj^able every six months, 
which will amortize a capital of $1. for one to one hundred semi-annual periods, 
at the following rates of compound interest. 


11/2% 

2% 

, 21/2% 

3% 

31/2% 

4 % 


5% 

51/2% 

6 % 


7% 


EXAMPLE.—What is the semi-annuity, payable every six months, which 
will amortize a capital of $1000 in 31 years, by sixty-two equal, semi-annual in¬ 
stalments @ 5V2% per annum compound interest? 


First Solution.— c=$1000; (7=1.0275; /i=62; q^=1.0215^ 


1000 X1.0275^ X (1.0275—1) 

1 . 0275®*''—1 


1000X5.376152X0.0275 

4.376152 


=$33.78406 


Second Solution. —Table IV, page 150, shows that the semi-annuity, which 
will amortize a capital of $1. in 31 years, by sixty-two equal, semi-annual instal¬ 
ments, @ 5V2% per annum, is 0.03378407; therefore the semi-annuity, which 
will amortize a capital of $1000, will be: 0.03378407X1000=$33.78407. 

139 






Rate, VAX to 2 V 2 X 
Years. 1 to 12 


TABLE IV 


SEMI-ANNUAL INSTALMENT 

The semi-annuity or semi-annual instalment payable every six months 
which will amortize a capital of $1 at a fixed rate of compound interest for one 
to one hundred semi-annual periods. 


Years Saitfeng* 1%% 2^0 2V2fc 


1 2 

3 

2 4 
S 

3 6 
7 

4 8 
9 


5 

10 


11 

6 

12 


13 

7 

14 


15 

8 

16 


17 

9 

18 


19 

10 

20 


21 

11 

22 


23 

12 

24 


25 


1.0075000 

0.5056402 

0.3383484 

0.2547063 

0.2045209 

0.1710697 

0.1471752 

0.1292573 

0.1153206 

0.1041694 

0.09504937 

0.08745054 

0.08102077 

0.07551057 

0.07073565 

0.06655795 

0.06287267 

0.05959713 

0.05666683 

0.05403012 

0.05164489 

0.04947708 

0.04749810 

0.04568426 

0.04401608 


1.0100000 

0.5075124 

0.3400221 

0.2562811 

0.2060400 

0.1725487 

0.1486290 

0.1306898 

0.1167406 

0.1055821 

0.09645360 

0.08884880 

0.08241444 

0.07690082 

0.07212338 

0.06794415 

0.06425789 

0.06098190 

0.05805151 

0.05541523 

0.05303057 

0.05086351 

0.04888558 

0.04707329 

0.04540663 


1.0125000 

0.5093993 

0.3417074 

0.2578625 

0.2075626 

0.1740342 

0.1500895 

0.1321333 

0.1181707 

0.1070037 

0.09786912 

0.09025904 

0.08382142 

0.07830574 

0.07352680 

0.06934713 

0.06566049 

0.06238506 

0.05945575 

0.05682074 

0.05443771 

0.05227271 

0.05029690 

0.04848684 

0.04682267 


140 




TABLE IV 


Rale, m%to 2^% 
Years, 13 to 25 


SEMI-ANNUAL INSTALMENT 

The semi-annuity or semi-annual instalment payable every six months 
which will amortize a capital of $i at a fixed rate of compound interest for one 
to one hundred semi-annual periods. 


Semi-Annual 
1 cars Instalments 


13 

26 


27 

14 

28 


29 

15 

30 


31 

16 

32 


33 

17 

34 


35 

18 

36 


37 

19 

38 


39 

20 

40 


41 

21 

42 


43 

22 

44 


45 

23 

46 


47 

24 

48 


49 

25 

50 


1 %% 


0.04247648 

0.04105138 

0.03972825 

0.03849697 

0.03734766 

0.03627301 

0.03526586 

0.03432002 

0.03343010 

0.03259125 

0.03179928 

0.03105041 

0.03034121 

0.02966857 

0.02902984 

0.02842242 

0.02784417 

0.02729304 

0.02676717 

0.02626492 

0.02578465 

0.02532508 

0.02488477 

0.02446265 

0.02405758 


2 % 


0.04386869 

0.04244541 

0.04112433 

0.03989492 

0.03874794 

0.03767561 

0.03667072 

0.03572731 

0.03483985 

0.03400355 

0.03321418 

0.03246792 

0.03176136 

0.03109148 

0.03045546 

0.02985093 

0.02927551 

0.02872726 

0.02820429 

0.02770491 

0.02722763 

0.02677101 

0.02633373 

0.02591465 

0.02551263 


2V2% 


0.04528748 

0.04386700 

0.04254886 

0.04132249 

0.04017876 

0.03910961 

0.03810810 

0.03716807 

0.03628407 

0.03545127 

0.03466548 

0.03392285 

0.03322001 

0.03255381 

0.03192154 

0.03132076 

0.03074919 

0.03020478 

0.02968570 

0.02919025 

0.02871688 

0.02826418 

0.02783088 

0.02741576 

0.02701773 


141 




Rate, iy2%to2y2% 
Yeara, 26 to 37 


TABLE IV 


SEMI-ANNUAL INSTALMENT 


The semi-annuity or semi-annual instalment payable every six months 
which will amortize a capital of $1 at a fixed rate of compound interest for one 
to one hundred semi-annual periods. 


Semi-Annual 
1 caib Instalments 



51 

26 

52 


53 

27 

54 


55 

28 

56 


57 

29 

58 


59 

30 

60 


61 

31 

62 


63 

32 

64 


65 

33 

66 


67 

34 

78 


69 

35 

70 


71 

36 

72 


73 

37 

74 


75 


11/2% 


0.02366860 

0.02329478 

0.02293523 

0.02258917 

0.02225584 

0.02193460 

0.02162477 

0.02132580 

0.02103706 

0.02075812 

0.02048849 

0.02022775 

0.01997539 

0.01973106 

0.01949436 

0.01926504 

0.01904267 

0.01882696 

0.01861765 

0.01841444 

0.01821708 

0.01802535 

0.01783900 

0.01765779 

0.01748154 


2fo 


0.02512670 

0.02475592 

0.02439947 

0.02405648 

0.02372627 

0.02340821 

0.02310145 

0.02280564 

0.02252011 

0.02224435 

0.02197791 

0.02172032 

0.02147116 

0.02123005 

0.02099659 

0.02077044 

0.02055129 

0.02033881 

0.02013272 

0.01993274 

0.01973862 

0.01955011 

0.01936698 

0.01918903 

0.01901602 


2 %% 


0.02663584 

0.02626907 

0.02591665 

0.02557771 

0.02525155 

0.02493747 

0.02463487 

0.02434312 

0.02406168 

0.02379003 

0.02352767 

0.02327419 

0.02302912 

0.02279212 

0.02256276 

0.02234073 

0.02212570 

0.02191733 

0.02171534 

0.02151948 

0.02132948 

0.02114509 

0.02096607 

0.02079222 

0.02062333 


142 





TABLE IV 


Rate, iy2%to2</2% 
Years, 38 to 50 


SEMI-ANNUAL INSTALMENT 

The semi-annuity or semi-annual instalment payable every six months 
which will amortize a capital of $1 at a fixed rate of compound interest for one 
to one hundred semi-annual periods. 


Semi-Annual 
1 cdib Instalments 


38 

76 


77 

39 

78 


79 

40 

80 


81 

41 

82 


83 

42 

84 


85 

43 

86 


87 

44 

88 


89 

45 

90 


91 

46 

92 


93 

47 

94 


95 

48 

96 


97 

49 

98 


99 

50 

100 




0.01731003 

0.01714312 

0.01698059 

0.01682228 

0.01666803 

0.01651773 

0.01637118 

0.01622829 

0.01608891 

0.01595292 

0.01582018 

0.01569061 

0.01556407 

0.01544047 

0.01531973 

0.01520175 

0.01508642 

0.01497366 

0.01486341 

0.01475557 

0.01465007 

0.01454683 

0.01444579 

0.01434689 

0.01425003 


2 % 


0.01884776 

0.01868408 

0.01852481 

0.01836977 

0.01821878 

0.01807172 

0.01792845 

0.01778880 

0.01765267 

0.01751992 

0.01739043 

0.01726415 

0.01714084 

0.01702049 

0.01690299 

0.01678825 

0.01667617 

0.01656666 

0.01645966 

0.01635505 

0.01625279 

0.01615278 

0.01605498 

0.01595930 

0.01586569 


21 / 2 % 


0.02045918 

0.02029961 

0.02014443 

0.01999346 

0.01984658 

0.01970362 

0.01956442 

0.01942888 

0.01929682 

0.01916814 

0.01904273 

0.01892047 

0.01880125 

0.01868496 

0.01857152 

0.01846082 

0.01835278 

0.01824729 

0.01814430 

0.01804371 

0.01794545 

0.01784946 

0.01775564 

0.01766395 

0.01757433 


143 




Rate, 3% to 4% 
Years, 1 to 12 


TABLE IV 


SEMI-ANNUAL INSTALMENT 


The semi-annuity or semi-annual instalment payable every six months 
which will amortize a capital of $1 at a fixed rate of compound interest for one 
to one hundred semi-annual periods. 


Semi-Annua! Oq/. 

1 ears instalments 0/0 



1 

1.0150000 

1 

2 

0.5112780 


3 

0.3433856 

2 

4 

0.2594471 


5 

0.2090893 

3 

6 

0.1755273 


7 

0.1515573 

4 

8 

0.1335854 


9 

0.1196112 

5 

10 

0.1084352 


11 

0.09929477 

6 

12 

0.09168084 


13 

0.08524082 

7 

14 

0.07972382 


15 

0.07494485 

8 

16 

0.07076563 


17 

0.06708008 

9 

18 

0.06380620 


19 

0.06087886 

10 

20 

0.05824611 


21 

0.05586580 

11 

22 

0.05370370 


23 

0.05173112 

12 

24 

0.04992439 


25 

0.04826375 


4^0 


1.0175000 

1.0200000 

0.5131666 

0.5150495 

0.3450682 

0.3467545 

0.2610324 

0.2626242 

0.2106226 

0.2121598 

0.1770231 

0.1785263 

0.1530308 

0.1545134 

0.1350428 

0.1365093 

0.1210582 

0.1225152 

0.1098756 

0.1113263 

0.1007303 

0.1021777 

0.09310410 

0.09455956 

0.08667296 

0.08811828 

0.08115582 

0.08260172 

0.07637753 

0.07782537 

0.07219965 

0.07365007 

0.06851640 

0.06996976 

0.06524493 

0.06670201 

0.06232077 

0.06378169 

0.05969134 

0.06115657 

0.05731479 

0.05878465 

0.05515650 

0.05663133 

0.05318806 

0.05466799 

0.05138577 

0.05287101 

0.04962960 

0.05122033 


144 




TABLE IV 


Rale, 3% to A% 
Years, 13 to 25 


SEMI-ANNUAL INSTALMENT 


The semi-annuity or semi-annual instalment payable every six months 
which will amortize a capital of $1 at a fixed rate of compound interest for one 
to one hundred semi-annual periods. 


Semi-Annual 
1 caib Instalments 


13 

26 


27 

14 

28 


29 

15 

30 


31 

16 

32 


33 

17 

34 


35 

18 

36 


37 

19 

38 


39 

20 

40 


41 

21 

42 


43 

22 

44 


45 

23 

46 


47 

24 

48 


49 

25 

50 


3% 


0.04673225 

0.04531552 

0.04400131 

0.04277902 

0.04163943 

0.04057449 

0.03957726 

0.03864164 

0.03776207 

0.03693383 

0.03615260 

0.03541456 

0.03471635 

0.03405481 

0.03342728 

0.03283123 

0.03226440 

0.03172480 

0.03121052 

0.03071951 

0.03025140 

0.02980358 

0.02937514 

0.02896492 

0.02857183 


3H% 


0.04818329 

0.04679090 

0.04548159 

0.04426430 

0.04312984 

0.04207013 

0.04107820 

0.04014786 

0.03927374 

0.03845090 

0.03767513 

0.03694263 

0.03624996 

0.03559405 

0.03497216 

0.03438177 

0.03382062 

0.03328672 

0.03277815 

0.03229326 

0.03183048 

0.03138841 

0.03096574 

0.03056130 

0.03017397 


49fc 


0.04969915 

0.04829299 

0.04698958 

0.04577828 

0.04464988 

0.04359629 

0.04261052 

0.04168651 

0.04081864 

0.04000212 

0.03923277 

0.03850669 

0.03782048 

0.03717106 

0.03655566 

0.03597181 

0.03541724 

0.03488987 

0.03438787 

0.03390955 

0.03345335 

0.03301785 

0.03260178 

0.03220390 

0.03182316 


15 


145 




Rate, 3% to 4^ 
Years, 26 to 37 


TABLE IV 


SEMI-ANNUAL INSTALMENT 


The semi-annuity or semi-annual instalment payable every six months 
which will amortize a capital of $1 at a fixed rate of compound interest for one 
to one hundred semi-annual periods. 


Semi-Annual 
I caib Instalments 



51 

26 

52 


53 

27 

54 


55 

28 

56 


57 

29 

58 


59 

30 

60 


61 

31 

62 


63 

32 

64 


65 

33 

66 


67 

34 

68 


69 

35 

70 


71 

36 

72 


73 

37 

74 


75 


3% 


0.02819481 

0.02783300 

0.02748550 

0.02715151 

0.02583030 

0.02652118 

0.02622351 

0.02593673 

0.02566023 

0.02539354 

0.02513615 

0.02488761 

0.02464751 

0.02441544 

0.02419104 

0.02397396 

0.02376384 

0.02356041 

0.02336337 

0.02317244 

0.02298735 

0.02280787 

0.02263376 

0.02246481 

0.02230081 


3%'?6 


0.02980276 

0.02944668 

0.02910497 

0.02877677 

0.02846133 

0.02815798 

0.02786611 

0.02758508 

0.02731434 

0.02705341 

0.02680177 

0.02655895 

0.02632458 

0.02609825 

0.02587954 

0.02566818 

0.02546376 

0.02526600 

0.02507462 

0.02488933 

0.02470988 

0.02453603 

0.02436752 

0.02420417 

0.02404573 


4% 


0.03145851 

0.03110903 

0.03077386 

0.03045222 

0.03014333 

0.02984651 

0.02956115 

0.02928662 

0.02902240 

0.02876791 

0.02852274 

0.02828639 

0.02805844 

0.02783850 

0.02762620 

0.02742118 

0.02722311 

0.02703168 

0.02684661 

0.02666761 

0.02649442 

0.02632678 

0.02616451 

0.02600732 

0.02585505 


146 




TABLE IV 


Rate, 3% to 4% 
Year*, 38 to 50 


SEMI-ANNUAL INSTALMENT 

The semi-annuity or semi-annual instalment payable every six months 
which will amortize a capital of $1 at a fixed rate of compound interest for one 
to one hundred semi-annual periods. 


V^jarQ Semi-Annual 
1 Instalments 


38 

76 


77 

39 

78 


79 

40 

80 


81 

41 

82 


83 

42 

84 


85 

43 

86 


87 

44 

88 


89 

45 

90 


91 

46 

92 


93 

47 

94 


95 

48 

96 


97 

49 

98 


99 

50 

100 


3 % 


0.02214154 

0.02198685 

0.02183653 

0.02169044 

0.02154840 

0.02141026 

0.02127589 

0.02114515 

0.02101791 

0.02089403 

0.02077340 

0.02065591 

0.02054144 

0.02042990 

0.02032120 

0.02021522 

0.02011188 

0.02001110 

0.01991279 

0.01981687 

0.01972327 

0.01963192 

0.01954274 

0.01945566 

0.01937063 


3 %% 


0.02389204 

0.02374288 

0.02359809 

0.02345750 

0.02332096 

0.02318830 

0.02305939 

0.02293408 

0.02281225 

0.02269377 

0.02257852 

0.02246638 

0.02235726 

0.02225105 

0.02214763 

0.02204693 

0.02194884 

0.02185329 

0.02176020 

0.02166946 

0.02158104 

0.02149482 

0.02141076 

0.02132878 

0.02124881 


4 % 


0.02570748 

0.02556443 

0.02542573 

0.02529120 

0.02516067 

0.02503402 

0.02491108 

0.02479170 

0.02467578 

0.02456317 

0.02445378 

0.02434746 

0.02424413 

0.02414369 

0.02404599 

0.02395097 

0.02385856 

0.02376863 

0.02368115 

0.02359598 

0.02351310 

0.02343240 

0.02335381 

0.02327727 

0.02320273 


147 




R»le,4Vi^frto5J/2:V 

Years, 1 to 12 


TABLE IV 


SEMI-ANNUAL INSTALMENT 

The serai-annuity or semi-annual instalment payable every six months 
v/hich will amortize a capital of $1 at a fixed rate of compound interest for one 
to one hundred semi-annual periods. 


Years 4%% 5% 5%>% 



1 

1 

2 


3 

2 

4 


5 

3 

6 


7 

4 

8 


9 

5 

10 


11 

6 

12 


13 

7 

14 


15 

8 

16 


17 

9 

18 


19 

10 

20 


21 

11 

22 


23 

12 

24 


25 


1.0225000 

0.5169405 

0.3484499 

0.2642224 

0.2137013 

0.1800354 

0.1560003 

0.1379853 

0.1239816 

0.1127878 

0.1036367 

0.09601762 

0.08957708 

0.08406256 

0.07928854 

0.07511682 

0.07144058 

0.06817739 

0.06526200 

0.06264217 

0.06027581 

0.05812833 

0.06617108 

0.05438035 

0.05273607 


1.0250000 

0.5188271 

0.3501397 

0.2658175 

0.2152471 

0.1815503 

0.1574952 

0.1394673 

0.1254569 

0.1142586 

0.1051058 

0.09748689 

0.09105481 

0.08553636 

0.08076622 

0.07659884 

0.07292762 

0.06966998 

0.06676050 

0.06414696 

0.06178720 

0.05964648 

0.05769627 

0.05591268 

0.05427583 


1.0275000 

0.5207204 

0.3518346 

0.2674211 

0.2167987 

0.1830711 

0.1589978 

0.1409582 

0.1269413 

0.1157400 

0.1065866 

0.09896882 

0.09253274 

0.08702472 

0.08225928 

0.07809724 

0.07443192 

0.07118075 

0.06827815 

0.06567186 

0.06331950 

0.06118648 

0.05924420 

0.05746873 

0.05584009 


148 




TABLE IV 


R«t*,4y3%to SVi% 
Years, 13 to 25 


SEMI-ANNUAL INSTALMENT 

The semi-annuity or semi-annual instalment payable every six months 
which will amortize a capital of $1 at a fixed rate of compound interest for one 
to one hundred semi-annual periods. 


Semi-Annual 
1 Cdib Instalments 


13 

26 


27 

14 

28 


29 

15 

30 


31 

16 

32 


33 

17 

34 


35 

18 

36 


37 

19 

38 


39 

20 

40 


41 

21 

42 


43 

22 

44 


45 

23 

46 


47 

24 

48 


49 

25 

50 


41/2 


0.05122144 

0.04982196 

0.04852536 

0.04732091 

0.04619940 

0.04515286 

0.04417421 

0.04325728 

0.04239662 

0.04158738 

0.04082528 

0.04010652 

0.03942762 

0.03878549 

0.03817741 

0.03760091 

0.03705369 

0.03653369 

0.03603906 

0.03556810 

0.03511926 

0.03469112 

0.03428236 

0.03389184 

0.03351840 


5% 


0.05276864 

0.05137678 

0.05008786 

0.04889119 

0.04777755 

0.04673890 

0.04576823 

0.04485930 

0.04400658 

0.04320549 

0.04245150 

0.04174083 

0.04107004 

0.04043608 

0.03983616 

0.03926781 

0.03872869 

0.03821683 

0.03773030 

0.03726744 

0.03682670 

0.03640663 

0.03600595 

0.03562342 

0.03525800 


51/2^0 


0.05434126 

0.05295786 

0.05167748 

0.05048945 

0.04938450 

0.04835460 

0.04739272 

0.04649261 

0.04564882 

0.04485652 

0.04411138 

0.04340959 

0.04274771 

0.04212263 

0.04153159 

0.04097207 

0.04044181 

0.03993877 

0.03946105 

0.03900697 

0.03857498 

0.03816363 

0.03777161 

0.03739777 

0.03704098 


149 




Rate,4y2%to5%% 
Years» 26 to 37 


TABLE IV 


SEMI-ANNUAL INSTALMENT 

The semi-annuity or semi-annual instalment payable every six months 
which will amortize a capital of $1 at a fixed rate of compound interest for one 
to one hundred semi-annual periods. 


Years SiTn'S' 41 / 2 % S% 



51 

26 

52 


53 

27 

54 


55 

28 

56 


57 

29 

58 


59 

30 

60 


61 

31 

62 


63 

32 

64 


65 

33 

66 


67 

34 

68 


69 

35 

70 


71 

36 

72 


73 

37 

74 


75 


0.03316105 

0.03281886 

0.03249097 

0.03217657 

0.03187494 

0.03158534 

0.03130716 

0.03103984 

0.03078271 

0.03053536 

0.03029726 

0.03006798 

0.02984706 

0.02963413 

0.02942881 

0.02923072 

0.02903957 

0.02885502 

0.02867679 

0.02850461 

0.02833819 

0.02817731 

0.02802172 

0.02787121 

0.02772555 


0.03490865 

0.03457442 

0.03425444 

0.03394793 

0.03365414 

0.03337238 

0.03310198 

0.03284239 

0.03259303 

0.03235336 

0.03212291 

0.03190122 

0.03168786 

0.03148244 

0.03128460 

0.03109394 

0.03091019 

0.03073296 

0.03056202 

0.03039709 

0.03023788 

0.03008414 

0.02993566 

0.02979218 

0.02965354 


0.03670019 

0.03637449 

0.03606302 

0.03576496 

0.03547958 

0.03520617 

0.03494409 

0.03469275 

0.03445158 

0.03422007 

0.03399772 

0.03378407 

0.03357871 

0.03338122 

0.03319125 

0.03300840 

0.03283240 

0.03266289 

0.03249958 

0.03234221 

0.03219050 

0.03204424 

0.03190314 

0.03176701 

0.03163563 


150 




TABLE IV 


Rate,4y2%to5y2% 
Year#, 38 to 50 


SEMI-ANNUAL INSTALMENT 

The semi-annuity or semi-annual instahnent payable every six months 
which will amortize a capital of $1 at a fixed rate of compound interest for one 
to one hundred semi-annual periods. 


Years S,4Tn'g‘ 4V2% 5% 5%% 


38 

76 


77 

39 

78 


79 

40 

80 


81 

41 

82 


83 

42 

84 


85 

43 

86 


87 

44 

88 


89 

45 

90 


91 

46 

92 


93 

47 

94 


95 

48 

96 


97 

49 

98 


99 

50 

100 


0.027584S8 

0.02744809 

0.02731591 

0.02718785 

0.02706377 

0.02694351 

0.02682694 

0.02671389 

0.02660424 

0.02649789 

0.02639468 

0.02629452 

0.02619731 

0.02610292 

0.02601128 

0.02592225 

0.02583578 

0.02575177 

0.02567013 

0.02559079 

0.02551366 

0.02543869 

0.02536579 

0.02529489 

0.02522594 


0.02951952 

0.02938993 

0.02926461 

0.02914335 

0.02902601 

0.02891245 

0.02880251 

0.02869606 

0.02859295 

0.02849308 

0.02839630 

0.02830252 

0.02821163 

0.02812350 

0.02803806 

0.02795521 

0.02778484 

0.02779688 

0.02772123 

0.02764783 

0.02757660 

0.02750744 

0.02744032 

0.02737514 

0.02731186 


0.03150881 

0.03138636 

0.03126809 

0.03115384 

0.03104345 

0.03093676 

0.03083362 

0.03073391 

0.03063748 

0.03054423 

0.03045401 

0.03036670 

0.03028220 

0.03020044 

0.03012127 

0.03004463 

0.02997040 

0.02989853 

0.02982892 

0.02976143 

0.02969607 

0.02963273 

0.02957135 

0.02951185 

0.02945419 


151 




Rate, 6X to 7% 
Year*, 1 to 12 


TABLE IV 


SEMI-ANNUAL INSTALMENT 

The semi-annuity or semi-annual instalment payable every six months 
which will amortize a capital of $1 at a fixed rate of compound interest for one 
to one hundred semi-annual periods. 


Years Sit?e"n'g' 6 % 61 / 2^0 lo/o 


1 

1 2 

3 

2 4 

5 


3 

6 


7 

4 

8 


9 

5 

10 


11 

6 

12 


13 

7 

14 


15 

8 

16 


17 

9 

18 


19 

10 

20 


21 

11 

22 


23 

12 

24 


25 


1.0300000 

0.5226108 

0.3535303 

0.2690271 

0.2183546 

0.1845985 

0.1605068 

0.1424568 

0.1284342 

0.1172308 

0.1080776 

0.1004622 

0.09402979 

0.08852656 

0.08376672 

0.07961095 

0.07595263 

0.07270883 

0.06981408 

0.06721580 

0.06487186 

0.06274751 

0.06081399 

0.05904751 

0.05742796 


1.0325000 

0.5245066 

0.3552313 

0.2706371 

0.2199149 

0.1861294 

0.1620219 

0.1439626 

0.1299356 

0.1187309 

0.1095793 

0.1019670 

0.09553909 

0.09004158 

0.08528836 

0.08113994 

0.07748950 

0.07425402 

0.07136792 

0.06877875 

0.06644410 

0.06432926 

0.06240546 

0.06064881 

0.05903920 


1.0350000 

0.5264011 

0.3569367 

0.2722527 

0.2214827 

0.1876691 

0.1*635451 

0.1454773 

0.1314464 

0.1202417 

0.1110924 

0.1034845 

0.09706190 

0.09157104 

0.08682834 

0.08268510 

0.07904332 

0.07581702 

0.07294045 

0.07036125 

0.06803674 

0.06593224 

0.06401896 

0.06227295 

0.06067418 


152 




TABLE IV 


Rale, to 1% 
Years, 13 to 25 


SEMI-ANNUAL INSTALMENT 


The semi-annuity or semi-annual instalment payable every six months 
which will amortize a capital of $1 at a fixed rate of compound interest for one 
to one hundred semi-annual periods. 


Years SfSI' 6% 6%% 


13 

26 


27 

14 

28 


29 

15 

30 


31 

16 

*32 


33 

17 

34 


35 

18 

36 


37 

19 

38 


39 

20 

40 


41 

21 

42 


43 

22 

44 


45 

23 

46 


47 

24 

48 


49 

25 

50 


0.05593841 

0.05456429 

0.05329331 

0.05211476 

0.05101934 

0.04999900 

0.04904670 

0.04815619 

0.04732203 

0.04653934 

0.04580384 

0.04511166 

0.04445939 

0.04384390 

0.04326242 

0.04271243 

0.04219171 

0.04169814 

0.04122990 

0.04078522 

0.04036256 

0.03996062 

0.03957780 

0.03921315 

0.03886552 


0.05755970 

0.05619578 

0.05493502 

0.05376672 

0.05268164 

0.05167165 

0.05072968 

0.04984953 

0.04902574 

0.04825341 

0.04752823 

0.04684640 

0.04620439 

0.04559914 

0.04502786 

0.04448808 

0.04397747 

0.04349396 

0.04303575 

0.04260104 

0.04218830 

0.04179614 

0.04142318 

0.04106824 

0.04073024 


0.05920550 

0.05785250 

0.05660278 

0.05544553 

0.05437144 

0.05337249 

0.05244161 

0.05157254 

0.05075976 

0.04999843 

0.04928423 

0.04861330 

0.04798222 

0.04738780 

0.04682736 

0.04629826 

0.04579833 

0.04532546 

0.04487770 

0.04445350 

0.04405113 

0.04366924 

0.04330650 

0.04296172 

0.04263375 


153 





Rate, e% io7% 
Years, 26 to 37 


TABLE IV 


SEMI-ANNUAL INSTALMENT 

The semi-annuity or semi-annual instalment payable every six months 
which will amortize a capital of $1 at a fixed rate of compound interest for one 
to one hundred semi-annual periods. 


Semi-Annual 
1 cars Instalments 



51 

26 

52 


53 

27 

54 


55 

28 

56 


57 

29 

58 


59 

30 

60 


61 

31 

62 


63 

32 

64 


65 

33 

66 


67 

34 

78 


69 

35 

70 


71 

36 

72 


73 

37 

74 


75 




0.03853386 

0.03821722 

0.03791473 

0.03762561 

0.03734910 

0.03708449 

0.03683116 

0.03658851 

0.03635596 

0.03613300 

0.03591913 

0.03571384 

0.03551685 

0.03532762 

0.03514584 

0.03497112 

0.03480314 

0.03464160 

0.03448622 

0.03433665 

0.03419269 

0.03405407 

0.03392055 

0.03379194 

0.03366798 


6 %% 


0.04040813 

0.04010100 

0.03980794 

0.03952817 

0.03926091 

0.03900550 

0.03876128 

0.03852764 

0.03830403 

0.03808990 

0.03788479 

0.03768823 

0.03749980 

0.03731909 

0.03714571 

0.03697933 

0.03681960 

0.03666621 

0.03651884 

0.03637724 

0.03624116 

0.03611030 

0.03598450 

0.03586347 

0.03574700 


7 % 


0.04232162 

0.04202433 

0.04174106 

0.04147095 

0.04121328 

0.04096735 

0.04073250 

0.04050814 

0.04029370 

0.04008866 

0.03989251 

0.03970485 

0.03952515 

0.03935311 

0.03918829 

0.03903035 

0.03887894 

0.03873380 

0.03859455 

0.03846099 

0.03833280 

0.03820976 

0.03809164 

0.03797819 

0.03786923 


154 





TABLE IV 


Rate, 6X to 7% 
Years, 38 to 50 


SEMI-ANNUAL INSTALMENT 


The semi-annuity or semi-annual instalment payable every six months 
which will amortize a capital of $1 at a fixed rate of compound interest for one 
to one hundred semi-annual periods. 


Vo.o»*c* Semi-Annual 
1 caib Instalments 


38 

76 


77 

39 

78 


79 

40 

80 


81 

41 

82 


83 

42 

84 


85 

43 

86 


87 

44 

88 


89 

45 

90 


91 

46 

92 


93 

47 

94 


95 

48 

96 


97 

49 

98 


99 

50 

100 


6 % 


0.03354852 

0.03343333 

0.03332225 

0.03321512 

0.03311176 

0.03301202 

0.03291576 

0.03282286 

0.03273315 

0.03264652 

0.03256284 

0.03248203 

0.03240394 

0.03232849 

0.03225557 

0.03218509 

0.03211697 

0.03205107 

0.03198738 

0.03192579 

0.03186620 

0.03180858 

0.03175281 

0.03169887 

0.03164668 


6 %% 


0.03563493 

0.03552707 

0.03542320 

0.03532320 

0.03522686 

0.03513406 

0.03504467 

0.03495852 

0.03487548 

0.03479541 

0.03471822 

0.03464378 

0.03457199 

0.03450276 

0.03443598 

0.03437152 

0.03430934 

0.03424931 

0.03419139 

0.03413548 

0.03408149 

0.03402935^ 

0.03397903 

0.03393044 

0.03388349 


7 % 


0.03776453 

0.03766393 

0.03756723 

0.03747427 

0.03738493 

0.03729897 

0.03721631 

0.03713678 

0.03706027 

0.03698664 

0.03691579 

0.03684758 

0.03678192 

0.03671870 

0.03665783 

0.03659920 

0.03654274 

0.03648834 

0.03643596 

0.03638548 

0.03633683 

0.03628997 

0.03624480 

0.03620124 

0.03615929 


155 






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n 



\ ft 


/ V 


: J 

•*.’* 


ft r. V >• s 


,-*a ' 


.<! 


•j " J-t. ;•/', • ! “ . 



ri>; 




> i 




4 

.'.f 


;’/i I 


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I 


( C'i / ft/'- • . -1. *• 







TABLE V 


ACTUAL VALUE OF AN AMOUNT 

OLATv-'VtAA?^ 




CC 


■VUAa*A-( 


€>-» ^ > 




The actual value of $1., or the capital of an amount of $1., payable after 
one to one hundred years at the following rates of compound discount. 


l</o 

VAio 

11/2% 

1%% 

2^0 

2%% 

21/2% 

2%% 

3% 

mio 

31 / 2 % 

3%% 

4% 


4%% 

4%% 

5<fo 


dV2<fo 

5%% 



7 % 

7y2% 

8<fo 


9 % 

91 / 2 % 


EXAMPLE.—What is the actual value today, of an amount of $1,000 to be 
received after 27 years, @ 5 compound discount, or what is the capital which 
invested @5% compound interest will amount to $1,000 after 27 years? 

5=1000. <7=1.05. n=27. <7”=1.05^ 

1000 


rjT. Table I, page 35, shows that 1.05 , or $1 invested 


Therefore, c— ^ 

5% per annum compound interest for 27 years becomes $3.733456. There¬ 


fore the equation will read: 

1000 1000 


T05^ 


.=1000-^3.733456=$267.8483 


3.733456 

Also Table V, page 175, shows that the actual value today or the capital, of an 
amount of $1. to be received after 27 years, @ 5% compound discount is 
0.2678483. Therefore for $1000 will be: 0.2678483 X1000=$267.8483. 

157 







Rate, 1% to mX 
Years, 1 to 25 


TABLE V 


COMPOUND DISCOUNT 


The actual value of $1 at a fixed rate of compound discount, payable after 
one to one hundred years. 


Years 

Ifo 

1%% 

IVafo 


1 

0.9900989 

0.9876542 

0.9852219 

0.9828010 

2 

0.9802962 

0.9754614 

0.9706620 

0.9658980 

3 

0.9705902 

0.9634190 

0.9563174 

0.9492854 

4 

0.9609804 

0.9515246 

0.9421849 

0.9329582 

5 

0.9514659 

0.9397774 

0.9282604 

0.9169130 

6 

0.9420452 

0.9281750 

0.9145432 

0.9011426 

7 

0.9327182 

0.9167164 

0.9010274 

0.8856438 

8 

0.9234830 

0.9053986 

0.8877124 

0.8704114 

9 

0.9143400 

0.8942208 

0.8745938 

0.8554414 

10 

0.9052870 

0.8831820 

0.8616684 

0.8407290 

11 

0.8963234 

0.8722784 

0.8489346 

0.8262689 

12 

0.8874494 

0.8615098 

0.8363890 

0.8120386 

13 

0.8786620 

0.8508736 

0.8240279 

0.7980916, 

14 

0.8699622 

0.8403694 

0.8118506 

0.7843654 

15 

0.8613486 

0.8299938 

0.7998529 

0.7708752 

16 

0.8528202 

0.8197474 

0.7880325 

0.7576165 

17 

0.8443772 

0.8096267 

0.7763865 

0.7445865 

18 

0.8360170 

0.7996316 

0.7649130 

0.7317802 

19 

0.8277392 

0.7897597 

0.7536090 

0.7191946 

20 

0.8195438 

0.7800099 

0.7424721 

0.7068250 

21 

0.8114294 

0.7703800 

0.7314995 

0.6946688 

22 

0.8033956 

0.7608693 

0.7206895 

0.6827212 

23 

0.7954410 

0.7514759 

0.7100392 

0.6709788 

24 

0.7875652 

0.7421982 

0.6995456 

0.6594388 

25 

0.7797677 

0.7330353 

158 

0.6892078 

0.6480970 





TABLE V 


Rate, 1% to 1%?^ 
Years, 26 to 50 


COMPOUND DISCOUNT 


The actual value of $1 at a fixed rate of compound discount, payable after 
one to one hundred years. 


Years 

Ifo 

11/4% 

1%% 

1%% 

26 

0.7720470 

0.7239855 

0.6790225 

0.6368036 

27 

0.7644033 

0.7150476 

0.6689876 

0.6259956 

28 

0.7568350 

0.7062200 

0.6591010 

0.6152288 

29 

0.7493415 

0.6975015 

0.6493609 

0.6046476 

30 

0.7419217 

0.6888901 

0.6397644 

0.5942484 

31 

0.7345763 

0.6803855 

0.6303096 

0.5840277 

32 

0.7273028 

0.6719858 

0.6209946 

0.5739831 

33 

0.7201022 

0.6636898 

0.6118176 

0.5641113 

34 

0.7129723 

0.6554960 

0.6027760 

0.5544095 

35 

0.7059132 

0.6474034 

0.5938683 

0.5448738 

36 

0.6989238 

0.6394107 

0.5850919 

0.5355026 

37 

0.6920036 

0.6315169 

0.5764453 

0.5262925 

38 

0.6851520 

0.6237206 

0.5679267 

0.5172410 

39 

0.6783686 

0.6160203 

0.5595335 

0.5083447 

40 

0.6716516 

0.6084151 

0.5512645 

0.4996018 

41 

0.6650018 

0.6009037 

0.5431179 

0.4910092 

42 

0.6584176 

0.5934851 

0.5350914 

0.4825643 

43 

0.6518984 

0.5861583 

0.5271837 

0.4742648 

44 

0.6454440 

0.5789217 

0.5193928 

0.4661080 

45 

0.6390533 

0.5717749 

0.5117172 

0.4580913 

46 

0.6327260 

0.5647158 

0.5041550 

0.4502126 

47 

0.6264617 

0.5577440 

0.4967046 

0.4424693 

48 

0.6202589 

0.5508586 

0.4893642 

0.4348593 

49 

0.6141179 

0.5440579 

0.4821321 

0.4273802 

50 

0.6080373 

0.5373409 

0.4750072 

0.4200297 


159 




Rate, 1% to 
Years, 51 to 75 


TABLE V 


COMPOUND DISCOUNT 

The actual value of $1 at a fixed rate of compound discount, payable after 
one to one hundred years. 


Years 1% 1%% 1%% 


51 

0.6020168 

0.5307074 

0.4679873 

0.4128056 

52 

0.5960563 

0.5241551 

0.4610713 

0.4057057 

53 

0.5901550 

0.5176843 

0.4542574 

0.3987281 

54 

0.5843118 

0.5112932 

0.4875443 

0.3918704 

55 

0.5785263 

0.5049808 

0.4409305 

0.3851306 

56 

0.5727984 

0.4987465 

0.4344143 

0.3785067 

57 

0.5671268 

0.4925893 

0.4279944 

0.3719968 

58 

0.5615120 

0.4865080 

0.4216694 

0.3655988 

59 

0.5559525 

0.4805017 

0.4154379 

0.3593109 

60 

0.5504478 

0.4745697 

0.4092985 

0.3531312 

61 

0.5449977 

0.4687109 

0.4032496 

0.3470576 

62 

0.5396017 

0.4629243 

0.3972903 

0.3410886 

63 

0.5342591 

0.4572091 

0.3914192 

0.3352222 

64 

0.5289696 

0.4515647 

0.3856347 

0.3294568 

65 

0.5237321 

0.4459898 

0.3799358 

0.3237904 

66 

0.5185455 

0.4404838 

0.3743209 

0.3182215 

67 

0.5134122 

0.4350459 

0.3687892 

0.3127485 

68 

0.5083292 

0.4296750 

0.3633389 

0.3073695 

69 

0.5032961 

0.4243703 

0.3579695 

0.3020830 

70 

0.4983130 

0.4191312 

0.3526793 

0.2968875 

71 

0.4933792 

0.4139568 

0.3474672 

0.2917814 

72 

0.4884939 

0.4088463 

0.3423323 

0.2867631 

73 

0.4836574 

0.4037987 

0.3372732 

0.2818311 

74 

0.4788690 

0.3988136 

0.3322888 

0.2769838 

75 

0.4741275 

0.3938901 

160 

0.3273784 

0.2722200 




TABLE V 


Rale, 1% to 
Years 76 to 100 


.COMPOUND DISCOUNT 


The actual value of $1 at a fixed rate of compound discount, payable after 
one to one hundred years. 


Years 

1% 



m^o 

76 

0.4694331 

0.3890273 

0.3225404 

0.2675381 

77 

0.4647851 

0.3842245 

0.3177738 

0.2629367 

78 

0.4601833 

0.3794810 

0.3130776 

0.2584145 

79 

0.4556270 

0.3747960 

0.3084510 

0.2539700 

80 

0.4511157 

0.3701690 

0.3038926 

0.2496020 

81 

0.4466493 

0.3655990 

0.2994015 

0.2453091 

82 

0.4422269 

0.3610853 

0.2949769 

0.2410899 

83 

0.4378484 

0.3566277 

0.2906177 

9.2369435 

84 

0.4335134 

0.3522249 

0.2863229 

0.2328683 

85 

0.4292210 

0.3478764 

0.2820915 

0.2288632 

86 

0.4249713 

0.3435806 

0.2779227 

0.2249270 

87 

0.4207637 

0.3393400 

0.2738151 

0.2210585 

88 

0.4165977 

0.3351506 

0.2697689 

0.2172565 

89 

0.4124729 

0.3310130 

0.2657822 

0.2135199 

90 

0.4083890 

0.3269264 

0.2618545 

0.2098476 

91 

0.4043455 

0.3228903 

0.2579847 

0.2062384 

92 

0.4003420 

0.3189041 

0.2541722 

0.2026914 

93 

0.3963785 

0.3149669 

0.2504160 

0.1992053 

94 

0.3924537 

0.3110785 

0.2467152 

0.1957791 

95 

0.3885680 

0.3072380 

0.2430693 

0.1924119 

96 

0.3847208 

0.3034450 

0.2394772 

0.1891027 

97 

0.3809118 

0.2996988 

0.2359381 

0.1858503 

98 

0.3771403 

0.2959987 

0.2324513 

0.1826539 

99 

0.3734061 

0.2923445 

0.2290161 

0.1795124 

100 

0.3697090 

0.2887355 

0.2256317 

0.1764250 


16 

161 






Rate, 2^10 2%^ 
Years, 1 to 25 


TABLE V 


COMPOUND DISCOUNT 


The actual value of $1 at a fixed rate of compound discount, payable after 
one to one hundred years. 


Years 

2% 

2%% 

21/2% 

2%% 

1 

0.9803920 

0.9779950 

0.9756097 

0.9732360 

2 

0.9611689 

0.9564747 

0.9518142 

0.9471884 

3 

0.9423224 

0.9354284 

0.9285999 

0.9218382 

4 

0.9238454 

0.9148444 

0.9059506 

0.8971660 

5 

0.9057314 

0.8947130 

0.8838542 

0.8731542 

6 

0.8879716 

0.8750246 

0.8622976 

0.8497852 

7 

0.8705616 

0.8557692 

0.8412650 

0.8270418 

8 

0.8534900 

0.8369392 

0.8207464 

0.8049069 

9 

0.8367550 

0.8185216 

0.8007284 

0.7833645 

10 

0.8203480 

0.8005104 

0.7811982 

0.7623983 

11 

0.8042624 

0.7828954 

0.7621445 

0.7419939 

12 

0.7884930 

0.7656680 

0.7435552 

0.7221348 

13 

0.7730325 

0.7488197 

0.7254198 

0.7028078 

14 

0.7578744 

0.7323422 

0.7077265 

0.6839978 

15 

0.7430144 

0.7162267 

0.6904648 

0.6656911 

16 

0.7284455 

0.7004667 

0.6736243 

0.6478747 

17 

0.7141623 

0.6850530 

0.6571943 

0.6305349 

18 

0.7001590 

0.6699786 

0.6411654 

0.6136596 

19 

0.6864303 

0.6552359 

0.6255271 

0.5972355 

20 

0.6729706 

0.6408169 

0.6102700 

0.5812514 

21 

0.6597750 

0.6267161 

0.5953855 

0.5656945 

22 

0.6468383 

0.6129253 

0.5808638 

0.5505543 

23 

0.6341551 

0.5994381 

0.5666965 

0.5358195 

24 

0.6217209 

0.5862475 

0.5528744 

0.5214789 

25 

0.6095301 

0.5733471 

162 

0.5393897 

0.5075222 




TABLE V 


R»te, 2% to 2%% 
Years, 26 to 50 


COMPOUND DISCOUNT 


The actual value of $1 at a fixed rate of compound discount, payable after 
one to one hundred years. 


Years 

2% 

2%% 

21/2% 

2%% 

26 

0.5975785 

0.5607308 

0.5262337 

0.4939389 

27 

0.5858611 

0.5483920 

0.5133988 

0.4807193 

28 

0.5743737 

0.5363250 

0.5008771 

0.4678533 

29 

0.5631115 

0.5245230 

0.4886604 

0.4553316 

30 

0.5520705 

0.5129807 

0.4767417 

0.4431451 

31 

0.5412454 

0.5016928 

0.4651136 

0.4312849 

32 

0.5306327 

0.4906530 

0.4537695 

0.4197420 

33 

0.5202282 

0.4798563 

0.4427020 

0.4085081 

34 

0.5100276 

0.4692971 

0.4319043 

0.3975747 

35 

0.5000265 

0.4589703 

0.4213699 

0.3869342 

36 

0.4902220 

0.4488708 

0.4110925 

0.3765781 

37 

0.4806098 

0.4389939 

0.4010658 

0.3664994 

38 

0.4711860 

0.4293338 

0.3912838 

0.3566904 

39 

0.4619470 

0.4198863 

0.3817403 

0.3471441 

40 

0.4528894 

0.4106463 

0.3724295 

0.3378532 

41 

0.4440091 

0.4016102 

0.3633458 

0.3288110 

42 

0.4353030 

0.3927732 

0.3544837 

0.3200107 

43 

0.4267678 

0.3841299 

0.3458378 

0.3114459 

44 

0.4183995 

0.3756773 

0.3374025 

0.3031104 

45 

0.4101956 

0.3674104 

0.3291732 

0.2949979 

46 

0.4021526 

0.3593257 

0.3211446 

0.2871027 

47 

0.3942672 

0.3514188 

0.3133118 

0.2794186 

48 

0.3865365 

0.3436859 

0.3056701 

0.2719403 

49 

0.3789572 

0.3361232 

0.2982147 

0.2646621 

50 

0.3715268 

0.3287268 

163 

0.2909411 

0.2575788 





Rate, 2% to 23/4% 
Years, 51 to 75 


TABLE V 


COMPOUND DISCOUNT 

The actual value of $1 at a fixed rate of compound discount, payable after 
one to one hundred years. 


Years 

2°lo 

214% 

2%% 

2%% 

51 

0.3642419 

0.3214930 

0.2838450 

0.2506850 

52 

0.3570997 

0.3144187 

0.2769219 

0.2439756 

53 

0.3500979 

0.3075000 

0.2701677 

0.2374456 

54 

0.3432333 

0.3007335 

0.2635781 

0.2310909 

55 

0.3365031 

0.2941159 

0.2571494 

0.2249060 

56 

0.3299049 

0.2876440 

0.2508777 

0.2188866 

57 

0.3234363 

0.2813143 

0.2447584 

0.2130283 

58 

0.3170944 

0.2751240 

0.2387887 

0.2073269 

59 

0.3108768 

0.2690700 

0.2329646 

0.2017780 

60 

0.3047811 

0.2631491 

0.2272825 

0.1963776 

61 

0.2988050 

0.2573587 

0.2217390 

0.1911218 

62 

0.2929461 

0.2516954 

0.2163307 

0.1860066 

63 

0.2872021 

0.2461569 

0.2110544 

0.1810283 

64 

0.2815707 

0.2407403 

0.2059067 

0.1761833 

65 

0.2760496 

0.2354430 

0.2008846 

0.1714680 

66 

0.2706369 

0.2302619 

0.1959849 

0.1668788 

67 

0.2653302 

0.2251950 

0.1912048 

0.1624124 

68 

0.2601276 

0.2202397 

0.1865413 

0.1580657 

69 

0.2550271 

0.2153933 

0.1819915 

0.1538352 

70 

0.2500265 

0.2106536 

0.1775526 

0.1497180 

71 

0.2451240 

0.2060182 

0.1732220 

0.1457109 

72 

0.2403176 

0.2014849 

0.1689971 

0.1418111 

73 

0.2356055 

0.1970512 

0.1648752 

0.1380157 

74 

0.2309857 

0.1927151 

0.1608538 

0.1343219 

75 

0.2264567 

0.1884745 

164 

0.1569306 

0.1307269 





TABLE V 


Rate, 2% to 2 %% 
Years, 76 to 100 


COMPOUND DISCOUNT 

The actual value of $1 at a fixed rate of compound discount, payable after 
one to one hundred years. 


Years 

2% 

2ViJo 

2%% 


76 

0.2220163 

0.1843271 

0.1531030 

0.1272281 

77 

0.2176630 

0.1802710 

0.1493687 

0.1238230 

78 

0.2133950 

0.1763042 

0.1457256 

0.1205090 

79 

0.2092109 

0.1724246 

0.1421713 

0.1172838 

80 

0.2051087 

0.1686305 

0.1387037 

0.1141448 

81 

0.2010869 

0.1649197 

0.1353207 

0.1110898 

82 

0.1971440 

0.1612907 

0.1320202 

0.1081166 

83 

0.1932785 

0.1577415 

0.1288001 

0.1052230 

84 

0.1894887 

0.1542705 

0.1256587 

0.1024068 

85 

0.1857732 

0.1508758 

0.1225938 

0.09966605 

86 

0.1821306 

0.1475557 

0.1196037 

0.09699854 

87 

0.1785594 

0.1443088 

0.1166865 

0.09440250 

88 

0.1750582 

0.1411333 

0.1138405 

0.09187586 

89 

0.1716257 

0.1380277 

0.1110639 

0.08941696 

90 

0.1682604 

0.1349904 

0.1083550 

0.08702380 

91 

0.1649612 

0.1320200 

0.1057122 

0.08469472 

92 

0.1617267 

0.1291149 

0.1031338 

0.08242792 

93 

0.1585556 

0.1262738 

0.1006184 

0.08022187 

94 

0.1554466 

0.1234951 

0.09816424 

0.07807485 

95 

0.1523986 

0.1207777 

0.09577002 

0.07598517 

96 

0.1494104 

0.1181199 

0.09343422 

0.07395155 

97 

0.1464808 

0.1155207 

0.09115530 

0.07197227 

98 

0.1436087 

0.1129787 

0.08893196 

0.07004602 

99 

0.1407927 

0.1104926 

0.08676286 

0.06817130 

100 

0.1380320 

0.1080613 

0.08464670 

0.06634678 


165 





Rate, 3X to 
Years, 1 to 25 


TABLE V 


COMPOUND DISCOUNT 


The actual value of $1 at a fixed rate of compound discount, payable after 
one to one hundred years. 


Years 

3% 

31 / 4-56 

SViifc 

3%% 

1 

0.9708737 

0.9685229 

0.9661837 

0.9638552 

2 

0.9425960 

0.9380370 

0.9335107 

0.9390174 

3 

0.9151416 

0.9085102 

0.9019436 

0.8954380 

4 

0.8884870 

0.8799130 

0.8714428 

0.8630726 

5 

0.8626088 

0.8522156 

0.8419740 

0.8318776 

6 

0.8374852 

0.8253902 

0.8135014 

0.8018094 

7 

0.8130922 

0.7994097 

0.7859917 

0.7728285 

8 

0.7894097 

0.7742467 

0.7594129 

0.7448950 

9 

0.7664175 

0.7498759 

0.7337317 

0.7179710 

10 

0.7440947 

0.7262717 

0.7089197 

0.6920206 

11 

0.7224218 

0.7034112 

0.6849469 

0.6670076 

12 

0.7013803 

0.6812693 

0.6617846 

0.6428986 

13 

0.6809520 

0.6598250 

0.6394056 

0.6196613 

14 

0.6611185 

0.6390557 

0.6177831 

0.5972638 

15 

0.6418624 

0.6189398 

0.5968919 

0.5756765 

16 

0.6231676 

0.5994576 

0.5767071 

0.5548689 

17 

0.6050170 

0.5805883 

0.5572049 

0.5348131 

18 

0.5873953 

0.5623135 

0.5383624 

0.5154826 

19 

0.5702867 

0.5446134 

0.5201567 

0.4968507 

20 

0.5536764 

0.5274704 

0.5025671 

0.4788926 

21 

0.5375499 

0.5108671 

0.4855722 

0.4615831 

22 

0.5218931 

0.4947867 

0.4691520 

0.4448995 

23 

0.5066925 

0.4792122 

0.4532867 

0.4288187 

24 

0.4919345 

0.4641281 

0.4379584 

0.4133192 

25 

0.4776064 

0.4495184 

0.4231482 

0.3983801 


166 




TABLE V 

COMPOUND DISCOUNT 


Rate, Z% to 3%%- 
Years, 26 to 50 


The actual value of $1 at a fixed rate of compound discount, payable after 
one to one hundred years. 


Years 

3% 

3y4% 

3%% 

3%% 

26 

0.4636956 

0.4353688 

0.4088387 

0.3839808 

27 

0.4501899 

0.4216648 

0.3950134 

0.3701020 

28 

0.4370775 

0.4083920 

0.3816556 

0.3567247 

29 

0.4243472 

0.3955371 

0.3687495 

0.3438311 

30 

0.4119877 

0.3830867 

0.3562797 

0.3314035 

31 

0.3999880 

0.3710283 

0.3442315 

0.3194250 

32 

0.3883380 

0.3593494 

0.3325908 

0.3078795 

33 

0.3770271 

0.3480382 

0.3213440 

0.2967513 

34 

0.3660458 

0.3370829 

0.3104772 

0.2860253 

35 

0.3553842 

0.3264724 

0.2999781 

0.2756871 

36 

0.3450331 

0.3161960 

0.2898339 

0.2657226 

37 

0.3349837 

0.3062431 

0.2800328 

0.2561181 

38 

0.3252269 

0.2966035 

0.2705631 

0.2468609 

39 

0.3157542 

0.2872672 

0.2614136 

0.2379382 

40 

0.3065576 

0.2782249 

0.2525736 

0.2293380 

41 

0.2976287 

0.2694672 

0.2440325 

0.2210487 

42 

0.2889600 

0.2609851 

0.2357802 

0.2130590 

43 

0.2805436 

0.2527701 

0.2278070 

0.2053580 

44 

0.2723725 

0.2448136 

0.2201034 

0.1979355 

45 

0.2644393 

0.2371076 

0.2126603 

0.1907812 

46 

0.2567372 

0.2296443 

0.2054690 

0.1838855 

47 

0.2492594 

0.2224157 

0.1985207 

0.1772390 

48 

0.2419994 

0.2154148 

0.1918075 

0.1708328 

49 

0.2349510 

0.2086341 

0.1853213 

0.1646581 

50 

0.2281077 

0.2020668 

0.1790544 

0.1587066 


167 





Rale, 3% to 
Years, 51 to 75 


TABLE V 

COMPOUND DISCOUNT 


The actual value of $1 at a fixed rate of compound discount, payable after 
one to one hundred years. 


Years 

3% 

31 / 4 % 

31 / 2 % 

S%<^0 

51 

0.2214638 

0.1957064 

0.1729994 

0.1529702 

52 

0.2150133 

0.1895461 

0.1671492 

0.1474412 

53 

0.2087509 

0.1835798 

0.1614969 

0.1421120 

54 

0.2026703 

0.1778012 

0.1560356 

0.1369754 

55 

0.1967677 

0.1722045 

0.1507591 

0.1320245 

56 

0.1910367 

0.1667840 

0.1456610 

0.1272525 

57 

0.1854725 

0.1615341 

0.1407352 

0.1226530 

58 

0.1800704 

0.1564495 

0.1359761 

0.1182198 

59 

0.1748256 

0.1515250 

0.1313779 

0.1139468 

60 

0.1697337 

0.1467554 

0.1269352 

0.1098282 

61 

0.1647900 

0.1421359 

0.1226427 

0.1058585 

62 

0.1599898 

0.1376619 

0.1184954 

0.1020323 

63 

0.1553304 

0.1333287 

0.1144883 

0.09834439 

64 

0.1508062 

0.1291319 

0.1106167 

0.09478979 

65 

0.1464138 

0.1250672 

0.1068761 

0.09136366 

66 

0.1421493 

0.1211305 

0.1032619 

0.08806134 

67 

0.1380090 

0.1173176 

0.09976992 

0.08487840 

68 

0.1339893 

0.1136248 

0.09639607 

0.08181058 

69 

0.1300868 

0.1100483 

0.09313640 

0.07885354 

70 

0.1262978 

0.1065842 

0.08998688 

0.07600339 

71 

0.1226193 

0.1032293 

0.08694382 

0.07325625 

72 

0.1190479 

0.0999799 

0.08400368 

0.07060845 

73 

0.1155805 

0.09683289 

0.08116302 

0.06805633 

74 

0.1122140 

0.09378487 

0.07841840 

0.06559648 

75 

0.1089457 

0.09083276 

0.07576657 

0.06322554 


168 





TABLE V 


Rate, 3% to 3%% 
Years, 76 to 100 


COMPOUND DISCOUNT 


The actual value of $1 at a fixed rate of compound discount, payable after 
one to one hundred years. 


Years 

3% 

3Vi<fo 

3%% 

3%% 

76 

0.1057725 

0.08797366 

0.07320442 

0.06094028 

77 

0.1026917 

0.08520450 

0.07072890 

0.05873764 

79 

0.0997007 

0.08252249 

0.06833710 

0.05661460 

79 

0.0967968 

0.07992494 

0.06602620 

0.05456826 

80 

0.09397757 

0.07740907 

0.06379346 

0.05259591 

81 

0.09124029 

0.07497247 

0.06163621 

0.05069486 

82 

0.08858282 

0.07261257 

0.05955188 

0.04886250 

83 

0.08600270 

0.07032693 

0.05753805 

0.04709648 

84 

0.08349780 

0.06811326 

0.05559234 

0.04539410 

85 

0.08106586 

0.06596923 

0.05371243 

0.04375338 

86 

0.07870470 

0.06389270 

0.05189605 

0.04217192 

87 

0.07641234 

0.06188153 

0.05014109 

0.04064755 

88 

0.07418672 

0.05993367 

0.04844549 

0.03917846 

89 

0.07202598 

0.05804711 

0.04680724 

0.03776236 

90 

0.06992818 

0.05622001 

0.04522442 

0.03639745 

91 

0.06789142 

0.05445036 

0.04369507 

0.03508190 

92 

0.06591401 

0.05273644 

0.04221748 

0.03381387 

93 

0.06399417 

0.05107644 

0.04078984 

0.03259168 

94 

0.06213027 

0.04946871 

0.03941049 

0.03141367 

95 

0.06032067 

0.04791157 

0.03807777 

0.03027823 

96 

0.05856375 

0.04640345 

0.03679012 

0.02918384 

97 

0.05685801 

0.04494280 

0.03554602 

0.02812900 

98 

0.05520196 

0.04352815 

0.03434398 

0.02711229 

99 

0.05359413 

0.04215801 

0.03318258 

0.02613233 

100 

0.05203317 

0.04083101 

0.03206048 

0.02518779 


169 





Rate, 4/0 to 
Years, 1 to 25 


TABLE V 


COMPOUND DISCOUNT 


The actual value of $1 at a fixed rate of compound discount, payable after 
one to one hundred years. 


Years 

4^6 

41 / 4^0 

4y2% 

4%% 

1 

0.9615384 

0.9592324 

0.9569377 

0.9546540 

2 

0.9245562 

0.9201274 

0.9157300 

0.9113642 

3 

0.8889964 

0.8826164 

0.8762966 

0.8700372 

4 

0.8548048 

0.8466340 

0.8385620 

0.8305846 

5 

0.8219278 

0.8121188 

0.8024519 

0.7929484 

6 

0.7903152 

0.7790110 

0.7678957 

0.7569652 

7 

0.7599187 

0.7472524 

0.7348285 

0.7226400 

8 

0.7306908 

0.7167890 

0.7031850 

0.6898712 

9 

0.7025877 

0.6875673 

0.6729045 

0.6585880 

10 

0.6755648 

0.6595366 

0.6439277 

0.6287239 

11 

0.6495817 

0.6326491 

0.6161987 

0.6002137 

12 

0.6245979 

0.6068576 

0.5896640 

0.5729967 

13 

0.6005749 

0.5821175 

0.5642715 

0.5470134 

14 

0.5774758 

0.5583864 

0.5399729 

0.5222085 

15 

0.5552654 

0.5356220 

0.5167202 

0.4985286 

16 

0.5339090 

0.5137862 

0.4944693 

0.4759223 

17 

0.5133740 

0.4928404 

0.4731763 

0.4543410 

18 

0.4936291 

0.4727489 

0.4528003 

0.4337386 

19 

0.4746432 

0.4534757 

0.4333018 

0.4140701 

20 

0.4563878 

0.4349887 

0.4146427 

0.3952938 

21 

0.4388343 

0.4172553 

0.3967874 

0.3773689 

22 

0.4219563 

0.4002449 

0.3797007 

0.3602567 

23 

0.4057270 

0.3839281 

0.3633500 

0.3439205 

24 

0.3901224 

0.3682763 

0.3477032 

0.3283253 

25 

0.3751177 

0.3532623 

170 

0.3327304 

0.3134368 




TABLE V 


Rate, 4% to 4%% 
Years, 26 to 50 


COMPOUND DISCOUNT 


The actual value of $1 at a fixed rate of compound discount, payable after 
one to one hundred years. 


Years 

4fo 

414% 

4%% 

4%% 

26 

0.3606901 

0.3388609 

0.3184023 

0.2992246 

27 

0.3468173 

0.3250464 

0.3046913 

0.2856551 

28 

0.3334782 

0.3117950 

0.2915706 

0.2727018 

29 

0.3206521 

0.2990849 

0.2790149 

0.2603358 

30 

0.3083196 

0.2868911 

0.2669999 

0.2485307 

31 

0.2964611 

0.2791953 

0.2555023 

0.2372608 

32 

0.2850588 

0.2639762 

0.2444998 

0.2265020 

33 

0.2740951 

0.2532146 

0.2339710 

0.2162310 

34 

0.2635529 

0.2428917 

0.2238958 

0.2064259 

35 

0.2534163 

0.2329896 

0.2142543 

0.1970652 

36 

0.2436694 

0.2234912 

0.2050280 

0.1881290 

37 

0.2342977 

0.2143800 

0.1961991 

0.1795982 

38 

0.2252862 

0.2056403 

0.1877503 

0.1714542 

39 

0.2166213 

0.1972569 

0.1796654 

0.1636794 

40 

0.2082898 

0.1892152 

0.1719286 

0.1562572 

41 

0.2002786 

0.1815014 

0.1645250 

0.1491715 

42 

0.1925757 

0.1741021 

0.1574401 

0.1424072 

43 

0.1851689 

0.1670044 

0.1506604 

0.1359496 

44 

0.1780470 

0.1601960 

0.1441727 

0.1297848 

45 

0.1711991 

0.1536652 

0.1379643 

0.1238996 

46 

0.1646145 

0.1474007 

0.1320232 

0.1182813 

47 

0.1582833 

0.1413915 

0.1263380 

0.1129177 

48 

0.1521955 

0.1356273 

0.1208976 

0.1077973 

49 

0.1463417 

0.1300982 

0.1156915 

0.1029091 

50 

0.1407133 

0.1247944 

0.1107095 

0.09824265 


171 





Rate, 4% to 4%% 
Years, 51 to 75 


TABLE V 

COMPOUND DISCOUNT 


The actual value of $1 at a fixed rate of compound discount, payable after 
one to one hundred years. 


Years 

4^ 

41 / 4 % 

4%fo 

4%'/o 

51 

0.1353013 

0.1197068 

0.1059421 

0.09378769 

52 

0.1300973 

0.1148267 

0.1013800 

0.08953482 

53 

0.1250936 

0.1101455 

0.09701437 

0.08547476 

54 

0.1202824 

0.1056551 

0.09283672 

0.08159884 

55 

0.1156561 

0.1013478 

0.08883896 

0.07789867 

56 

0.1112078 

0.09721612 

0.08501342 

0.07436625 

57 

0.1069305 

0.09325287 

0.08135254 

0.07099408 

58 

0.1028178 

0.08945118 

0.07784932 

0.06777478 

59 

0.09886337 

0.08580450 

0.07449694 

0.06470146 

60 

0.09506092 

0.08230648 

0.07128895 

0.06176749 

61 

0.09140474 

0.07895109 

0.06821906 

0.05896658 

62 

0.08788920 

0.07573245 

0.06528139 

O.05629268 

63 

0.08450884 

0.07264502 

0.06247026 

0.05374004 

64 

0.08125854 

0.06968345 

0.05978017 

0.05130315 

65 

0.07813320 

0.06684261 

0.05720588 

0.04897676 

66 

0.07512809 

0.06411764 

0.05474248 

0.04675587 

67 

0.07223858 

0.06150371 

0.05238516 

0.04463566 

68 

0.06946018 

0.05899635 

0.05012931 

0.04261161 

69 

0.06678863 

0.05659124 

0.04797062 

0.04067934 

70 

0.06421984 

0.05428414 

0.04590489 

0.03883470 

71 

0.06174984 

0.05207111 

0.04392813 

0.03707372 

72 

0.05937488 

0.04994830 

0.04203649 

0.03539255 

74 

0.05709123 

0.04791203 

0.04022631 

0.03378766 

74 

0.05489540 

0.04595880 

0.03849407 

0.03225551 

75 

0.05278404 

0.04408517 

0.03683643 

0.03079286 


172 




TABLE V 


Rate, 4% to 4%% 
Years, 76 to 100 


COMPOUND DISCOUNT 

Tbe actual value of $1 at a fixed rate of compound discount, payable after 
one to one hundred years. 


Years 4%% 


76 0.05075390 

77 0.04880182 

78 0.04692484 

79 0.04512002 

80 0.04338464 


0.04228793 

0.04056396 

0.03891027 

0.03732400 

0.03580240 


0.03525017 

0.03373222 

0.03227963 

0.03088960 

0.02955943 


0.02939653 

0.02806351 

0.02679094 

0.02557607 

0.02441631 


81 0.04171598 0.03434283 

82 0.04011154 0.03294277 

83 0.03856879 0.03159977 

84 0.03708539 0.03031152 

85 0.03565902 0.02907579 


0.02828653 

0.02706844 

0.02590282 

0.02478739 

0.02371999 


0.02330913 

0.02225215 

0.02124310 

0.02027981 

0.01936020 


86 0.03428752 

87 0.03296879 

88 0.03170074 

89 0.03048150 

90 0.02930914 


0.02789045 

0.02675342 

0.02566276 

0.02461656 

0.02361299 


0.02269855 

0.02172110 

0.02078575 

0.01989066 

0.01903413 


0.01848230 

0.01764420 

0.01684411 

0.01608030 

0.01535112 


91 0.02818187 

92 0.02709796 

93 0.02605572 

94 0.02505359 

95 0.02408999 


0.02265036 

0.02172696 

0.02084121 

0.01999156 

0.01917655 


0.01821447 0.01465501 
0.01743012 0.01399046 
0.01667954 0.01335605 
0.01596128 0.01275041 
0.01527395 0.01217223 


96 0.02316345 

97 0.02227255 

98 0.02141591 

99 0.02059223 
100 0.01980022 


0.01839477 

0.01764486 

0.01692553 

0.01623552 

0.01557364 


0.01461623 

0.01398682 

0.01338451 

0.01280814 

0.01225660 


0.01162026 

0.01109333 

0.01059029 

0.01011007 

0.009651614 


173 





Rat®, 5% to S%X 
Years, 1 to 25 


TABLE V 


COMPOUND DISCOUNT 


The actual value of $1 at a fixed rate of compound discount, payable after 
one to one hundred years. 


Years 

5% 

51 / 4 % 

51 / 2 % 

5%% 

1 

0.9523809 

0.9501187 

0.9478672 

0.9456264 

2 

0.9070294 

0.9027256 

0.8984522 

0.8942094 

3 

0.8638376 

0.8576966 

0.8516134 

0.8455880 

4 

0.8227024 

0.8149137 

0.8072166 

0.7996104 

5 

0.7835262 

0.7742649 

0.7651340 

0.7361327 

6 

0.7462133 

0.7356435 

0.7232433 

0.7150190 

7 

0.7106813 

0.6989486 

0.6874363 

0.6761409 

8 

0.6768393 

0.6640843 

0.6515983 

0.6393767 

9 

0.6446090 

0.6309590 

0.6176287 

0.6046116 

10 

0.6139133 

0.5994860 

0.5854300 

0.5717365 

11 

0.5846793 

0.5695829 

0.5349099 

0.5406492 

12 

0.5568374 

0.5411714 

0.5259810 

0.3112522 

13 

0.5303214 

0.5141770 

0.4985601 

0.4834536 

14 

0.5050679 

0.4885293 

0.4725688 

0.4571665 

15 

0.4810171 

0.4641609 

0.4479324 

0.4323087 

16 

0.4381114 

0.4410080 

0.4245805 

0.4088026 

17 

0.4362967 

0.4190099 

0.4024459 

0.3865745 

18 

0.4153207 

0.3981092 

0.3814653 

0.3655350 

19 

0.3957339 

0.3782310 

0.3615784 

0.3456785 

20 

0.3768894 

0.3593834 

0.3427283 

0.3268828 

21 

0.3589423 

0.3414569 

0.3248610 

0.3091090 

22 

0.3418499 

0.3244246 

0.3079250 

0.2923016 

23 

0.3255713 

0.3082419 

0.2918720 

0.2764081 

24 

0.3100679 

0.2928664 

0.2766559 

0.2613788 

23 

0.2953027 

0.2782579 

174 

0.2622331 

0.2471667 




TABLE V 


Rate, S% to 5%?^ 
Years, 26 to 50 


COMPOUND DISCOUNT 


The actual value of $1 at a fixed rate of compound discount, payable after 
one to one hundred years. 


Years 

5% 

5%% 

5%% 

5%% 

26 

0.2812407 

0.2643781 

0.2485622 

0.2337274 

27 

0.2678483 

0.2511906 

0.2356039 

0.2210188 

28 

0.2550936 

0.2386609 

0.2233212 

0.2090012 

29 

0.2429463 

0.2267562 

0.2116789 

0.1976371 

30 

0.2313774 

0.2154453 

0.2006435 

0.1868908 

31 

0.2203595 

0.2046986 

0.1901833 

0.1767289 

32 

0.2098661 

0.1944880 

0.1802685 

0.1671195 

33 

0.1998726 

0.1847867 

0.1708707 

0.1580327 

34 

0.1903548 

0.1755693 

0.1619627 

0.1494398 

35 

0.1812903 

0.1668117 

0.1535191 

0.1413143 

36 

0.1726574 

0.1584909 

0.1455157 

0.1336305 

37 

0.1644356 

0.1505852 

0.1379296 

0.1263645 

38 

0.1566054 

0.1430738 

0.1307389 

0.1194936 

39 

0.1491479 

0.1359371 

0.1239232 

0.1129964 

40 

0.1420457 

0.1291564 

0.1174627 

0.1068523 

41 

0.1352816 

0.1227139 

0.1113391 

0.1010424 

42 

0.1288396 

0.1165928 

0.1055346 

0.09554834 

43 

0.1227044 

0.1107770 

0.1000328 

0.09035304 

44 

0.1168613 

0.1052513 

0.09481782 

0.08544024 

45 

0.1112965 

0.1000013 

0.08987472 

0.08079454 

46 

0.1059967 

0.09501309 

0.08518930 

0.07640145 

47 

0.1009429 

0.09027370 

0.08074814 

0.07224723 

48 

0.09614209 

0.08577074 

0.07653850 

0.06831889 

49 

0.09156390 

0.08149240 

0.07254835 

0.06460414 

50 

0.08720372 

0.07742747 

0.06876619 

0.06109140 




Rale, SX to S%% 
Years, 51 to 75 


TABLE V 


COMPOUND DISCOUNT 


The actual value of $1 at a fixed rate of compound discount, payable after 
one to one hundred years. 


Years 

5% 

51 / 4 % 

51 / 2^0 

5%fo 

51 

0.08305116 

0.07356529 

0.06518123 

0.05776963 

52 

0.07909634 

0.06989577 

0.06178314 

0.05462849 

53 

0.07532985 

0.06640928 

0.05856221 

0.05165815 

54 

0.07174272 

0.06309670 

0.05550920 

0.04884930 

55 

0.06832639 

0.05994935 

0.05261535 

0.04619319 

56 

0.06507276 

0.05695900 

0.04987237 

0.04368150 

57 

0.06197406 

0.05411783 

0.04727238 

0.04130639 

58 

0.05902290 

0.05141836 

0.04480794 

0.03906041 

59 

0.05621230 

0.04885354 

0.04247198 

0.03693655 

60 

0.05353551 

0.04641667 

0.04025780 

0.03492818 

61 

0.05098621 

0.04410135 

0.03815904 

0.03302902 

62 

0.04855829 

0.04190152 

0.03616971 

0.03123311 

63 

0.04624599 

0.03981142 

0.03428408 

0.02953485 

64 

0.04404380 

0.03782558 

0.03249675 

0.02792894 

65 

0.04194648 

0.03593879 

0.03080261 

0.02641034 

66 

0.03994903 

0.03414612 

0.02919678 

0.02497432 

67 

0.03804669 

0.03244287 

0.02767468 

0.02361638 

68 

0.03623494 

0.03082458 

0.02623192 

0.02233227 

69 

0.03450947 

0.02928701 

0.02486437 

0.02111798 

70 

0.03286616 

0.02782614 

0.02356812 

0.01996972 

71 

0.03130110 

0.02643814 

0.02233945 

0.01888390 

72 

0.02981058 

0.02511938 

0.02117483 

0.01785711 

73 

0.02839103 

0.02386639 

0.02007093 

0.01688615 

74 

0.02703907 

0.02267591 

0.01902457 

0.01596800 

75 

0.02575149 

0.02154480 

0.01803277 

0.01509976 




TABLE V 


Rate, 5%" toi 5%% 
Year*, 76 to 100 


COMPOUND DI3C0UNT 

; The actual value of $1 at a fixed rate of compound discount, payable after 
one to one hundred years. 


Years 5% 5%% 


76 0.02452524 

77 0.02335736 

78 0.02224511 

79 0.02118582 

80 0.02017697 

81 0.01921616 

82 0.01830111 

83 0.01742963 

84 0:01659965 

85 0.01580919 


0.02047012 

0.01944904 

0.01847890 

0.01755715 

0.01668138 

0.01584929 

0.01505871 

0.01430757 

0.01359389 

0.01291581 


0.01709267 

0.01620159 

0.01535695 

0.01455635 

0.01379749 

0.01307819 

0.01239638 

0.01175012 

0.01113756 

0.01055693 


0.01427873 

0^01350234 

0.01276817 

0.01207392 

0.01141742 

0.01079662 

0.01020957 

0.009654432 

0.009129488 

0.008633084 


86 0.01505637 

87 0,01433940 

88 0.01365657 

89 0.01300626 

90 0.01238691 


0.01227155 

0.01165943 

0.01107784 

0.01052527 

0.01000025 


0.01000656 

0.009484894 

0.008990420 

0.008521726 

0.008077464 


0.008163674 

0.007719785 

0.007300032 

0.006903103 

0.006527758 


91 

92 

93 

94 

95 


0.01179706 

0.01123530 

0.01070028 

0.01019074 

0.009705469 


0.009501429 

0.009027486 

0.008577184 

0.008149344 

0.007742844 


0.007656363 

0.007257215 

0.006878846 

0.006520262 

0.006180341 


0.006172820 

0.005837181 

0.005519794 

0.005219662 

0.004935850 


96 0.009243304 0.007356622 0.005858143 0.004667471 

97 0.008803146 0.006989665 0.005552743 0.004413684 

98 0.008383948 0.006641010 0.005263262 0.004173696 

99 0.007984714 0.006309749 0.004988873 0.003946757 
100 0.007604487 0.005995011 0.004728790 0.003732158 


17 


177 




Rate, 6% to 7% 
Years, 1 to 25 


TABLE V 


COMPOUND DISCOUNT 


The actual value of $1 at a fixed rate of compound discount, payable after 
one to one hundred years. 


Years 

6 % 


l<Jo 

1 

0.9433960 

0.9389672 

0.9345794 

2 

0.8899964 

0.8816594 

0.8734386 

3 

0.8396190 

0.8278490 

0.8162978 

4 

0.7920933 

0.7773232 

0.7628950 

5 

0.7472580 

0.7298808 

0.7129860 

6 

0.7049602 

0.6853342 

0.6663420 

7 

0.6650568 

0.6435063 

0.6227496 

8 

0.6274120 

0.6042313 

0.5820089 

9 

0.5918981 

0.5673533 

0.5439335 

10 

0.5583944 

0.5327261 

0.5083490 

11 

0.5267871 

0.5002123 

0.4750925 

12 

0.4969689 

0.4696830 

0.4440116 

13 

0.4688385 

0.4410170 

0.4149642 

14 

0.4423005 

0.4141004 

0.3878170 

15 

0.4172645 

0.3888266 

0.3624458 

16 

0.3936457 

0.3650954 

0.3387343 

17 

0.3713639 

0.3428126 

0.3165741 

18 

0.3503433 

0.3218897 

0.2958636 

19 

0.3905125 

0.3022440 

0.2765081 

20 

0.3118042 

0.2837971 

0.2584188 

21 

0.2941549 

0.2664762 

0.2415128 

22 

0.2775046 

0.2502123 

0.2257129 

23 

0.2617968 

0.2349412 

0.2109466 

24 

0.2469780 

0.2206021 

0.1971464 

25 

0.2329982 

0.2071381 

0.1842490 


178 




TABLE V 


Rate, 6% to 7^ 
Years, 26 to SO 


COMPOUND DISCOUNT 


The actual value of $1 at a fixed rate of compound discount, payable after 
one to one hundred years. 


Years 

6Yo 


7% 

26 

0.2198096 

0.1944959 

0.1721953 

27 

0.2073675 

0.1826253 

0.1609301 

28 

0.1956297 

0.1714791 

0.1504020 

29 

0.1845563 

0.1610132 

0.1405626 

30 

0.1741097 

0.1511861 

0.1313669 

31 

0.1642544 

0.1419588 

0.1227728 

32 

0.1549570 

0.1332947 

0.1147409 

33 

0.1461858 

0.1251593 

0.1072345 

34 

0.1379112 

0.1175205 

0.1002192 

35 

0.1301048 

0.1103479 

0.09366276 

36 

0.1227404 

0.1036130 

0.08753530 

37 

0.1157928 

0.09728924 

0.08180868 

38 

0.1092385 

0.09135140 

0.07645670 

39 

0.1030552 

0.08577596 

0.07145486 

40 

0.09722187 

0.08054082 

0.06678025 

41 

0.09171874 

0.07562517 

0.06241144 

42 

0.08652712 

0.07100955 

0.05832844 

43 

0.08162934 

0.06667565 

0.05451256 

44 

0.07700880 

0.06260623 

0.05094631 

45 

0.07264981 

0.05878520 

0.04761349 

46 

0.06853755 

0.05519738 

0.04449848 

47 

0.06465806 

0.05182851 

0.04158737 

48 

0.06099817 

0.04866528 

0.03886670 

49 

0.05754544 

0.04569509 

0.03632401 

50 

0.05428815 

0.04290620 

0.03394767 


179 





Rate, 6% to 7% 
Years, 51 to 75 


TABLE V 


COMPOUND DISCOUNT 


The actual value of $1 at a fixed rate of compound discount, payable after 
one to one hundred years. 


Years 

6 % 

6 ^2% 

7% 

51 

0.05121522 

0.04028751 

0.03172680 

52 

0.04831624 

0.03782864 

0.02965121 

53 

0.04558136 

0.03551986 

0.02771141 

54 

0.04300128 

0.03335198 

0.02589851 

55 

0.04056725 

0.03131641 

0.02420422 

56 

0.03827098 

0.02940508 

0.02262076 

57 

0.03610470 

0.02761041 

0.02114090 

58 

0.03406103 

0.02592527 

0.01975785 

59 

0.03213304 

0.02434297 

0.01846528 

60 

0.03031420 

0.02285725 

0.01725727 

61 

0.02859829 

0.02146221 

0.01612829 

62 

0.02697952 

0.02015230 

0.01507316 

63 

0.02545238 

0.01892236 

0.01408707 

64 

0.02401167 

0.01776747 

0.01316548 

65 

0.02265252 

0.01668307 

0.01230419 

66 

0.02137030 

0,01566485 

0.01149924 

67 

0.02016066 

0.01470878 

0.01074695 

68 

0.01901949 

0.01381107 

0.01004388 

69 

0.01794291 

0.01296814 

0.009386804 

70 

0.01692727 

0.01217666 

0.008772714 

71 

0.01596913 

0.01143348 

0.008198798 

72 

0.01506521 

0.01073566 

0.007662429 

73 

0.01421246 

0.01008044 

0.007161148 

74 

0.01340798 

0.009465197 

0.006692660 

75 

0.01264904 

0.008887508 

0.006254823 


180 




TABL£ V 

COMPOUND DISCOUNT 


Rate, 6% to 7”^ 
Years, 76 to 100 


^ The actual value of $1 at a fixed rate of compound discount, payable after 
one to one hundred years. 


Years 

696 

61/2% 

7% 

76 

0.01193305 

0.008345080 

0.005845628 

77 

0.01125760 

0.007835754 

0.005463204 

78 

0.01062037 

0.007357515 

0.005105797 

79 

0.01001922 

0.006908465 

0.004771773 

80 

0.009452094 

0.006486823 

0.004459601 

81 

0.008917068' 

0.006090913 

0.004167851 

82 

0.008412328 

0.005719167 

0.003895187 

83 

0.007936157 

0.005370110 

0.003640363 

84 

0.007486942 

0.005042357 

0.003402208 

85 

0.007063150 

0.004734608 

0.003179633 

86 

0.006663349 

0.004445641 

0.002971620 

87 

0.006286179 

0.004174311 

0.002777214 

88 

0.005930355 

0.003919541 

0.002595527 

89 

0.005594675 

0.003680320 

0.002425726 

90 

0.005277995 

0.003455700 

0.002267034 

91 

0.004979240 

0.003244789 

0.002118723 

92 

0.004697397 

0.003046750 

0.001980115 

93 

0.004431505 

0.002860798 

0.001850574 

94 

0.004180666 

0.002686196 

0.001729509 

95 

0.003944024 

0.002522249 

0.001616343 

96 

0.003720777 

0.002368309 

0.001510620 

97 

0.003510166 

0.002223765 

0.001411794 

98 

0.003311478 

0.002088042 

0.001319434 

99 

0.003124035 

0.001960603 

0.001233116 

100 

0.002947203 

0.001840942 

0.001152445 


181 





Rale. 71 / 2 % to 8 y 2 % 
Year*, 1 to 25 


TABLE V 


COMPOUND DISCOUNT 


The actual value of $1 at a fixed rate of compound discount, payable after 
one to one hundred years. 


Years 

7y2% 

00 

8 %% 

1 

0.9302326 

0.9259256 

0.9216592 

2 

0.8653324 

0.8573386 

0.8494554 

3 

0.8049604 

0.7938320 

0.7829084 

4 

0.7488003 

0.7350295 

0.7215745 

5 

0.6965583 

0.6805828 

0.6650456 

6 

0.6479611 

0.6301693 

0.6129454 

7 

0.6027546 

0.5834900 

0.5649267 

8 

0.5607018 

0.5402684 

0.5206697 

9 

0.5215831 

0.5002485 

0.4798800 

10 

0.4851936 

0.4631930 

0.4422858 

11 

0.4513428 

0.4288824 

0.4076367 

12 

0.4198537 

0.3971133 

0.3757021 

13 

0.3905615 

0.3676974 

0.3462692 

14 

0.3633130 

0.3404605 

0.3191422 

15 

0.3379655 

0.3152412 

0.2941403 

16 

0.3143866 

0.2918900 

0.2710970 

17 

0.2924526 

0.2702685 

0.2498591 

18 

0.2720490 

0.2502486 

0.2302848 

19 

0.2530687 

0.2317116 

0.2122441 

20 

0.2354128 

0.2145478 

0.1956167 

21 

0.2189886 

0.1986553 

0.1802917 

22 

0.2037103 

0.1839401 

0.1661677 

23 

0.1894980 

0.1703149 

0.1531500 

24 

0.1762772 

0.1576990 

0.1411521 

25 

0.1639787 

0.1460175 

0.1300941 


182 





TABLE V 


Rale, 7 ^ 3 % to 8 ^ 2 % 
Years, 26 to 50 


COMPOUND DISCOUNT 


The actual value of $1 at a fixed rate of compound discount, payable after 
one to one hundred years. 


Years 

71 / 2 % 

00 

Wo 

26 

0.1525384 

0.1352014 

0.1199024 

27 

0.1418961 

0.1251865 

0.1105091 

28 

0.1319964 

0.1159134 

0.1018517 

29 

0.1227873 

0.1073272 

0.09387257 

30 

0.1142207 

0.09937702 

0.08651850 

31 

0.1062519 

0.09201574 

0.07974055 

32 

0.09883892 

0.08519976 

0.07349362 

33 

0.09194317 

0.07888865 

0.06773606 

34 

0.08552852 

0.07304505 

0.06242954 

35 

0.07956142 

0.06763430 

0.05753875 

36 

0.07401062 

0.06262434 

0.05303112 

37 

0.06884708 

0.05798549 

0.04887661 

38 

0.06404379 

0.05369027 

0.04504757 

39 

0.05957561 

0.04971321 

0.04151850 

40 

0.05541916 

0.04603074 

0.03826590 

41 

0.05155271 

0.04262106 

0.03526812 

42 

0.04795600 

0.03946394 

0.03250518 

43 

0.04461023 

0.03654068 

0.02995869 

44 

0.04149789 

0.03383396 

0.02761170 

45 

0.03860268 

0.03132774 

0.02544858 

46 

0.03590947 

0.02900716 

0.02345491 

47 

0.03340415 

0.02685848 

0.02161744 

48 

0.03107363 

0.02486896 

0.01992390 

49 

0.02890570 

0.02302681 

0.01836305 

50 

0.02688902 

0.02132112 

0.01692447 


183 





Rate, 71 / 2 % to 81 / 2 % 
-Years, ^ 51 to 75 


TABLE V 


•COMPOUND DISCOUNT 


The actual value of $1 at a fixed rate of compound discount, payable after 
one to one hundred years. 


Years 


8f> 

8V2% 

51 

0.02501304 

0.01974178 

0.01559859 

52 

0.02326794 

0.01827942 

0.01437658 

53 

0.02164460 

0.01692529 

0.01325031 

54 

0.02013450 

0.01567165 

0.01221226 

55 

0.01872977 

0.01451079 

0.01125554 

56 

0.01742304 

0.01343591 

0.01037377 

57 

0.01620748 

0.01244066 

0.009561082 

58 

0.01507672 

0.01151913 

0.008812060 

59 

0.01402486 

0.01066586 

0.008121716 

60 

0.01304638 

0.009875792 

0.007485452 

61 

0.01213616 

0.009144252 

0.006899035 

62 

0.01128945 

0.008466900 

0.006358557 

63 

0.01050182 

0.007839722 

0.005860421 

64 

0.009769132 

0.007259000 

0.005401311 

65 

0.009087564 

0.006721295 

0.004978168 

66 

0.008453548 

0.006223421 

0.004588173 

67 

0.007863764 

0.005762427 

0.004228731 

68 

0.007315129 

0.005335580 

0.003897449 

69 

0.006804770 

0.004940351 

0.003592119 

70 

0.006330019 

0.004574398 

0.003310709 

71 

0.005888389 

0.004235554 

0.003051345 

72 

0.005477571 

0.003921809 

0.002812300 

73 

0.005095414 

0.003631304 

0.002591982 

74 

0.004739920 

0.003362318 

0.002388923 

75 

0.004409227 

0.003113257 

0.002201773 


184 




TABLE V 


Rate, 7V2%ioSV2X 
Years,. 76 to 100 ^ 


COMPOUND DISCOUNT 


. The actual value of $1 at a fixed rate of compound discount, payable after 
one to one hundred years. 


Years 

7%% 

8% 

8V2(fo 

76 

0.004101607 

0.002882652 

0.002029284 

77 

0.003815447 

0.002669116 

0.001870308 

78 

0.003549253 

0.002471403 

0.001723786 

79 

0.003301631 

0.002288336 

0.001588743 

80 

0.003071284 

0.002118829 

0.001464279 

81 

0.002857009 

0.001961879 

0.001349567 

82 

0.002657682 

0.001816554 

0.001243840 

83 

0.002472262 

0.001681995 

0.001146397 

84 

0.002299778 

0.001557402 

0.001056587 

85 

0.002139328 

0.001442039 

0.0009738129 

86 

0.001990073 

0.001335221 

0.0008975234 

87 

0.001851230 

0.001236316 

0.0008272106 

88 

0.001722075 

0.001144737 

0.0007624062 

89 

0.001601930 

0.001059941 

0.0007026785 

90 

0.001490167 

0.000981427 

0.0006476300 

91 

0.001386202 

0.0009087286 

0.0005968941 

92 

0.001289490 

0.0008414152 

0.0005501329 

93 

0.001199525 

0.0007790882 

0.0005070349 

94 

0.001115837 

0.0007213778 

0.0004673133 

95 

0.001037988 

0.0006679423 

0.0004307036 

96 

0.0009655704 

0.0006184651 

0.0003969619 

97 

0.0008982050 

0.0005726528 

0.0003658635 

98 

0.0008355396 

0.0005302330 

0.0003372014 

99 

0.0007772460 

0.0004909573 

0.0003107847 

100 

0.0007230195 

0.0004545901 

0.0002864376 


185 




Rale, 9^10 S^% 
Years, 1 to 25 


TABLE V 

COMPOUND DISCOUNT 


The actual value of $1 at a fixed rate of compound discount, payable after 
one to one hundred years. 


Years 9% 


1 

0.9174312 

0.9132420 

2 

0.8416800 

0.8340110 

3 

0.7721835 

0.7616540 

4 

0.7084252 

0.6955742 

5 

0.6499313 

0.6352277 

6 

0.5962673 

0.5801168 

7 

0.5470342 

0.5297870 

8 

0.5018662 

0.4838238 

9 

0.4604277 

0.4418482 

10 

0.4224108 

0.4035144 

11 

0.3875329 

0.3685063 

12 

0.3555347 

0.3365354 

13 

0.3261787 

0.3073383 

14 

0.2992464 

0.2806743 

15 

0.2745381 

0.2563235 

16 

0.2518698 

0.2340854 

17 

0.2310732 

0.2137766 

18 

0.2119937 

0.1952298 

19 

0.1944896 

0.1782921 

20 

0.1784309 

0.1628238 

21 

0.1636980 

0.1486976 

22 

0.1501817 

0.1357969 

23 

0.1377813 

0.1240154 

24 

0.1264049 

0.1132561 

25 

0.1159678 

0.1034302 


186 




TABLE V 


Rate, 9% to 
Years, 26 to 50 


COMPOUND DISCOUNT 


The actual value of $1 at a fixed rate of compound discount, payable after 
one to one hundred years. 


Years 

9% 

m°io 

26 

0.1063925 

0.09445682 

27 

0.09760780 

0.08626196 

28 

0.08954844 

0.07877804 

29 

0.08215452 

0.07194343 

30 

0.07537112 

0.06570176 

31 

0.06914783 

0.06000161 

32 

0.06343837 

0.05479599 

33 

0.05820034 

0.05004200 

34 

0.05339480 

0.04570046 

35 

0.04898606 

0.04173559 

36 

0.04494134 

0.03811469 

37 

0.04123059 

0.03480793 

38 

0.03782623 

0.03178807 

39 

0.03470296 

0.02903021 

40 

0.03183757 

0.02651161 

41 

0.02920879 

0.02421151 

42 

0.02679705 

0.02211097 

43 

0.02458445 

0.02019267 

44 

0.02255454 

0.01844079 

45 

0.02069224 

0.01684091 

46 

0.01898371 

0.01537982 

47 

0.01741624 

0.01404550 

48 

0.01597821 

0.01282694 

49 

0.01465890 

0.01171410 

50 

0.01344854 

0.01069781 


187 





Rate, 9% to 9V2% 
Year*, 51 to 75. 


TABLE V 


COMPOUND DISCOUNT 


The actual value of $1 at a fixed rate of compound discount, payable after 
one to one hundred years. 


Years 

9% 

91 / 2^0 

51 

0.01233810 

0.009769692 

52 

0.01131936 

0.008922094 

53 

0.01038474 

0.008148032 

54 

0.009527282 

0.007441125 

55 

0.008740626 

0.006795548 

56 

0.008018922 

0.006205980 

57 

0.007356810 

0.005667563 

58 

0.006749366 

0.005175856 

59 

0.006192078 

0.004726810 

60 

0.005680807 

0.004316721 

61 

0.005211739 

0.003942211 

62 

0.004781421 

0.003600193 

63 

0.004386625 

0.003287848 

64 

0.004024426 

0.003002601 

65 

0.003692134 

0.002742101 

66 

0.003387280 

0.002504202 

67 

0.003107596 

0.002286843 

68 

0.002851005 

0.002088532 

69 

0.002615601 

0.001907336 

70 

0.002399634 

0.001741860 

71 

0.002201499 

0.001590739 

72 

0.002019724 

0.001452730 

73 

0.001852958 

0.001326694 

74 

0.001699961 

0.001211592 

75 

0.001559598 

188 

0.001106477 




TABLE V 


Rate, 9% to 
Years, 76 to 100 


COMPOUND DISCOUNT 


The actual value of $1 at a fixed rate of compound discount, payable after 
one to one hundred years. 

Years 

9^0 

91 / 2 % 

76 

0.001430823 

0.001010482 

77 

0.001312682 

0.0009228142 

78 

0.001204295 

0.0008427528 

79 

0.001104858 

0.0007696374 

80 

0.001013631 

0.0007028652 

81 

0.0009299370 

0.0006418860 

82 

0.0008531532 

0.0005861973 

83 

0.0007827094 

0.0005353400 

84 

0.0007180820 

0.0004888950 

85 

0.0006587908 

0.0004464795 

86 

0.0006043951 

0.0004077438 

87 

0.0005544910 

0.0003723688 

88 

0.0005087073 

0.0003400629 

89 

0.0004667040 

0.0003105597 

90 

0.0004281688 

0.0002836162 

91 

0.0003928154 

0.0002590102 

92 

0.0003603811 

0.0002365390 

93 

0.0003306248 

0.0002160173 

94 

0.0003033255 

0.0001972761 

95 

0.0002782803 

0.0001801609 

96 

0.0002553031 

0.0001645305 

97 

0.0002342230 

0.0001502562 

98 

0.0002148834 

0.0001372203 

99 

0.0001971408 

0.0001253153 

100 

0.0001808631 

0.0001144432 


189 






) ■ 













TABLE VI 

ACTUAL VALUE OF AN ANNUITY 


c=— 

cT 

The actual value of an annuity, or an annual instalment of $1. payable for 
one to one hundred years, at the following rates of compound discount. 


1^0 

lVi% 


1%% 

2% 

2Vi<jb 

2V2 <^o 

2%% 

3 % 


ZV2^0 

33/4% 

4% 


iV2^0 

4%% 

5% 


51 / 2 % 

5%<fo 

6% 

ev2% 

7 fo 

71/2% 

8% 


9 % 

91/2% 


EXAMPLE.—What is the actual value of an annuity of $1000, to be received 
every year for 53 years @ per annum compound discount; or what is the 
capital which will be amortized by an annuity of $1000, payable every year @ 
3^i% per annum compound interest for 53 years? 

5=1000. <7=1.0325. n=53. <7”=1.0325“ 

Therefore C= ^ 03^1^ ’ Table I, page 24, shows that 1.0325“ or $1. invested 

@ 3%% per annum compound interest for 53 years, becomes $5.447224; there¬ 
fore the equation will read: 

C=-T4^STS-=^T^^rr=1000H-5.447224=$183.6798 


1.0325“ 5.447224 

For the 52nd year it wiU be: 

1000 1000 


1.0325“ “ 5.275761 
For the 51st year it will be: 


=1000-^^5.275761=$189.5461 


C= 


1000 


1000 


1.0325' 




5.109696 


•=1000-^-5.109696=$195.7064 


And so on until the first year, and by adding all these fifty-three actual values 
together the result is, $25120.5565. 

Also Table VI, page 202, shows that the actual value today of an annuity 
of $1. or the capital which will be amortized by an annuity of $1. payable every 
year for 53 years @ 3^% per annum compound interest is: $25.1205565; there¬ 
fore for an annuity of $1000 it will be: 25.1205565X1000=$25120.5565. 

191 









Rate, 1% to 13/4^ 
Years, 1 to 25 


TABLE VI 


ACTUAL VALUE OF AN ANNUITY 


The actual value of an annuity or an annual instalment of $1 payable for 
one to one hundred years at a fixed rate of compound discount. 


Years 

1% 

1%% 

.U/2% 

13/4% 

1 

0.9900989 

0.9876542 

0.9852219 

0.9828010 

2 

1.9703951 

1.9631156 

1.9558839 

1.9486990 

3 

2.9409853 

2.9265346 

2.9122013 

2.8979844 

4 

3.9019657 

3.8780592 

3.8543862 

3.8309426 

5 

4.8534316 

4.8178366 

4.7826466 

4.7478556 

6 

5.7954768 

5.7460116 

5.6971898 

5.6489982 

7 

6.7281950 

6.6627280 

6.5982172 

6.5346420 

8 

7.6516780 

7.5681266 

7.4859296 

7.4050534 

9 

8.5660180 

8.4623474 

8.3605234 

8.2604948 

1 10 

9.4713050 

9.3455294 

9.2221918 

9.1012238 

11 

10.3676284 

10.2178078 

10.0711264 

9.9274927 

12 

11.2550778 

11.0793176 

10.9075154 

10.7395313 

13 

12.1337398 

11.9301912 

11.7315433 

11.5376229 

14 

13.0037020 

12.7705606 

12.5433939 

12.3219883 

15 

13.8650506 

13.6005544 

13.3432468 

13.0928635 

16 

14.7178708 

14.4203018 

14.1312793 

13.8504800 

17 

15.5622480 

15.2299285 

14.9076658 

14.5950665 

18 

16.3982560 

16.0295601 

15.6725788 

15.3268467 

19 

17.2260042 

16.8193198 

16.4261878 

16.0460413 

20 

18.0455480 

17.5993297 

17.1686599 

16.7528663 

21 

18.8569774 

18.3697097 

17.9001594 

17.4475351 

22 

19.6603730 

19.1305790 

18.6208489 

18.1302563 

23 

20.4558140 

19.8820549 

19.3308881 

18.8012351 

24 

21.2433792 

20.6242531 

20.0304337 

19.4606739 

25 

22.0231469 

21.3572884 

20.7196415 

20.1087709 


i92 




TABLE VI 


Rate. 1% to 1%% 
Years, 26 to 50 


ACTUAL VALUE OF AN ANNUITY 


The actual value of an annuity or an annual instalment of $1 payable for 
one to one hundred years at a fixed rate of compound discount. 


Years 

1% 

1%% 

1%% 

1%% 

26 

22.7951939 

22.0812739 

21.3986640 

20.7455745 

27 

23.5595972 

22.7963215 

22.0676516 

21.3715701 

28 

24.3164322 

23.5025415 

22.7267526 

21.9867989 

29 

25.0657737 

24.2000430 

23.3761135 

22.5914465 

30 

25.8076954 

24.8889331 

24.0158779 

23.1856949 

31 

26.5422717 

25.5693186 

24.6461875 

23.7697226 

32 

27.2695745 

26.2413044 

25.2671821 

24.3437057 

33 

27.9896767 

26.9049942 

25.8789997 

24.9078170 

34 

28.7026490 

27.5604902 

26.4817757 

25.4622265 

35 

29.4085622 

28.2078936 

27.0756440 

26.0071003 

36 

30.1074860 

28.8473043 

27.6607359 

26.5426029 

37 

30.7994896 

29.4788212 

28.2371812 

27.0688954 

38 

31.4846416 

30.1025418 

28.8051079 

27.5861364 

39 

32.1630102 

30.7185621 

29.3646414 

28.0944811 

40 

32.8346618 

31.3269772 

29.9159059 

28.5940829 

41 

33.4996636 

31.9278809 

30.4590238 

29.0850921 

42 

34.1580812 

32.5213660 

30.9941152 

29.5676564 

43 

34.8099796 

33.1075243 

31.5212989 

30.0419212 

44 

35.4554236 

33.6864460 

32.0406917 

30.5080292 

45 

36.0944769 

34.2582209 

32.5524089 

30.9661205 

46 

36.7272029 

34.8229367 

33.0565639 

31.4163331 

47 

37.3536646 

35.3806807 

33.5532685 

31.8588024 

48 

37.9739235 

35.9315393 

34.0426327 

32.2936617 

49 

38.5880414 

36.4755972 

34.5247648 

32.7210419 

50 

39.1960787 

37.0129381 

34.9997720 

33.1410716 


18 


193 




Rate. l%to 
YearSi' 51 to 75 


TABLE VI 


ACTUAL VALUE OF AN ANNUITY 


The actual value of an annuity or an annual instalment of $1 payable for 
one to one hundred years at a fixed rate of compound discount. 


Years 

1 % 

l%fo 

1V2^0 

l%9fc 

51 

39.7980955 

37.5436455 

35.4677593 

33.5538772 

52 

40.3941518 

38.0678006 

35.9288306 

33.9595829 

53 

40.9843068 

38.5854849 

36.3830880 

34.3583110 

54 

41.5686186 

39.0967781 

36.8306323 

34.7501814 

55 

42.1471449 

39.6017589 

37.2715682 

35.1353120 

56 

42.7199433 

40.1005054 

37.7059771 

35.5138187 

57 

43.2870701 

40.5930947 

38.1339715 

35.8858155 

58 

43.8485821 

41.0796027 

38.5556409 

36.2514143 

59 

44.4045346 

41.5601044 

38.9710788 

36.6107252 

60 

44.9549824 

42.0346741 

39.3803773 

36.9638564 

61 

45.4999801 

42.5033850 

39.7836269 

37.3109140 

62 

46.0395818 

42.9663093 

40.1809172 

37.6520026 

63 

46.5738409 

43.4235184 

40.5723364 

37.9872248 

64 

47.1028105 

43.8750831 

40.9579711 

38.3166816 

65 

47.6265426 

44.3210729 

41.3379069 

38.6404720 

66 

48.1450881 

44.7615567 

41.7122278 

38.9586935 

67 

48.6585003 

45.1966026 

42.0810170 

39.2714420 

68 

49.1668295 

45.6262776 

42.4443559 

39.5788115 

69 

49.6701256 

46.0506479 

42.8023254 

39.8808945 

70 

50.1684386 

46.4697791 

43.1550047 

40.1777820 

71 

50.6618178 

46.8837359 

43.5024719 

40.4695634 

72 

51.1503117 

47.2925882 

44.8448042 

40.7563265 

73 

51.6339691 

47.6963809 

44.1820774 

41.0381576 

74 

52.1128381 

49.0951945 

44.5143662 

41.3151414 

75 

52.5869656 

48.4890846 

44.8417446 

41.5873614 


194 




TABLE VI 


Rate, 1% to 13/4^ 
Years 76 to 100 


ACTUAL VALUE OF AN ANNUITY 


The actual value of an annuity or an annual instalment of $1 payable for 
one to one hundred years at a fixed rate of compound discount. 


Years 

1% 

1%% 

1%% 

1%^0 

76 

53.0563987 

48.8781119 

45.1642850 

41.8548995 

77 

53.5211838 

49.2623364 

45.4820588 

42.1178362 

78 

53.9813671 

49.6418174 

45.7951364 

42.3762507 

79 

54.4369941 

50.0166134 

46.1035874 

42.6302207 

80 

54.8881098 

50.3867824 

46.4074800 

42.8798227 

81 

55.3347591 

50.7523814 

46.7068815 

43.1251318 

82 

55.7769860 

51.1134667 

47.0018584 

43.3662217 

83 

56.2148344 

51.4700944 

47.2924761 

43.6031652 

84 

56.6483478 

51.8223193 

47.5787990 

43.8360335 

85 

57.0775688 

52.1701957 

47.8608905 

44.0648967 

86 

57.5025401 

52.5137763 

48.1388132 

44.2898237 

87 

57.9233038 

52.8531163 

48.4126283 

44.5108822 

88 

58.3399015 

53.1882669 

48.6823972 

44.7281387 

89 

58.7523744 

53.5192799 

48.9481794 

44.9416586 

90 

59.1607634 

53.8462063 

49.2100339 

45.1515062 

91 

59.5651089 

54.1690966 

49.4680186 

45.3577446 

92 

59.9654509 

54.4880007 

49.7221908 

45.5604360 

93 

60.3618294 

54.8029676 

49.9726068 

45.7596413 

94 

60.7542831 

55.1140461 

50.2193220 

45.9554204 

95 

61.1428511 

55.4212841 

50.4623913 

46.1478323 

96 

61.5275719 

55.7247291 

50.7018685 

46.3369350 

97 

61.9084837 

56.0244279 

50.9378066 

46.5227853 

98 

62.2856240 

56.3204266 

51.1702579 

46.7054392 

99 

62.6590301 

56.6127711 

51.3992740 

46.8849516 

100 

63.0287391 

56.9015066 

51.6249057 

47.0613766 




Rate, 2% to 2%% 
Years, 1 to 25 


TABLE VI 


ACTUAL VALUE OF AN ANNUITY 


The actual value of an annuity or an annual instalment of $1 payable for 
one to one hundred years at a fixed rate of compound discount. 


Years 

2<fo 

21/4% 

21 /2% 

2 %% 

1 

0.9803920 

0.9779950 

0.9756097 

0.9732360 

2 

1.9415609 

1.9344697 

1.9274239 

1.9204244 

3 

2.8838833 

2.8698981 

2.8560238 

2.8422626 

4 

3.8077287 

3.7847425 

3.7619744 

3.7394286 

5 

4.7134601 

4.6794555 

4.6458286 

4.6125828 

6 

5.6014317 

5.5544801 

5.5081262 

5.4623680 

7 

6.4719933 

6.4102493 

6.3493912 

6.2894098 

8 

7.3254833 

7.2471885 

7.1701376 

7.0943167 

9 

8.1622383 

8.0657101 

7.9708660 

7.8776812 

10 

8.9825863 

8.8662205 

8.7520642 

8.6400795 

11 

9.7868487 

9.6491159 

9.5142087 

9.3820734 

12 

10.5753417 

10.4147839 

10.2577639 

10.1042082 

13 

11.3483742 

11.1636036 

10.9831837 

10.8070160 

14 

12.1062486 

11.8959458 

11.6909102 

11.4910138 

15 

12.8492630 

12.6121725 

12.3813750 

12.1567049 

16 

13.5777085 

13.3126392 

13.0549993 

12.8045796 

17 

14.2918708 

13.9976922 

13.7121936 

13.4351145 

18 

14.9920298 

14.6676708 

14.3533590 

14.0487741 

19 

15.6784601 

15.3229067 

14.9788861 

14.6460096 

20 

16.3514307 

15.9637236 

15.5891561 

15.2272610 

21 

17.0112057 

16.5904397 

16.1845316 

15.7929555 

22 

17.6580440 

17.2033650 

16.7654054 

16.3435098 

23 

18.2921991 

17.8028031 

17.3321019 

16.8793293 

24 

18.9139200 

18.3890506 

17.8849763 

17.4008082 

25 

19.5234501 

18.9623977 

18.4243660 

17.9083304 


196 




TABLE VI 

ACTUAL VALUE OF AN ANNUITY 


Rate, 2% to 2%% 
Years, 26 to 5Q 


The actual value of an annuity or an annual instalment of $1 payable for 
one to one hundred years at a fixed rate of compound discount. 


Years 

2 % 

2y4% 


2 %% 

26 

20.1210286 

19.5231285 

18.9505997 

18.4022693 

27 

20.7068897 

20.0715205 

19.4639985 

18.8829886 

28 

21.2812634 

20.6078455 

19.9648756 

19.3508419 

29 

21.8443749 

21.1323685 

20.4535360 

19.8061735 

30 

22.3964454 

21.6453492 

20.9302777 

20.2493186 

31 

22.9376908 

21.1470420 

21.3953913 

20.6806035 

32 

23.4683235 

22.6376950 

21.8491608 

21.1003455 

33 

23.9885517 

23.1175513 

22.2918628 

21.5088536 

34 

24.4985793 

23.5868484 

22.7237671 

21.9064283 

35 

24.9986058 

24.0458187 

23.1451370 

22.2933625 

36 

25.4888278 

24.4946895 

23.5562295 

22.6699406 

37 

25.9694376 

24.9336834 

23.9572953 

23.0364400 

38 

26.4406236 

25.3630172 

24.3485791 

23.3931304 

39 

26.9025706 

25.7829035 

24.7303194 

23.7402745 

40 

27.3554600 

26.1935498 

24.1027489 

24.0781277 

41 

27.7994691 

26.5951600 

25.4660947 

24.4069387 

42 

28.2347721 

26.9879332 

25.8205784 

24.7269494 

43 

28.6615399 

27.3720631 

26.1664162 

25.0383953 

44 

29.0799394 

27.7477404 

26.5038187 

25.3415057 

45 

29.4901350 

28.1151508 

26.8329919 

25.6365036 

46 

29.8922876 

28.4744765 

27.1541365 

25.9236063 

47 

30.2865548 

28.8258953 

27.4674483 

26.2030249 

48 

30.6730913 

29.1695812 

27.7731184 

26.4749652 

49 

31.0520485 

29.5057044 

28.0713331 

26.7396273 

50 

31.4235753 

29.8344312 

28.3622742 

26.9972061 


197 




Rate. 2%to2%% 
■tear*. 51 to 75 


TABLE VI 

ACTUAL VALUE OF AN ANNUITY 


The actual value of an annuity or an annual instalment of $1 payable for 
one to one hundred years at a fixed rate of compound discount. 


Years 

2% 

2%% 

2%% 

2%% 

51 

31.7878172 

30.1559242 

28.6461192 

27.2478911 

52 

32.1449169 

30.4703429 

28.9230411 

27.4918677 

58 

32.4950148 

30.7778429 

29.1932088 

27.7293123 

54 

32.8382481 

31.0785764 

29.4567869 

27.9604032 

55 

33.1747512 

31.3726923 

29.7139363 

28.1853092 

56 

33.5046561 

31.6603363 

29.9648140 

28.4041958 

57 

33.8280924 

31.9416506 

30.2095724 

28.6172241 

58 

34.1451868 

32.2167746 

30.4483611 

28.8245510 

59 

34.4560636 

32.4858446 

30.6813257 

29.0263290 

60 

34.7608447 

32.7489937 

30.9086082 

29.2227066 

61 

35.0596497 

33.0063524 

31.1303472 

29.4138284 

62 

35.3525958 

33.2580478 

31.3466779 

29.5998350 

63 

35.6397979 

33.5042047 

31.5577323 

29.7808633 

64 

35.9213686 

33.7449450 

31.7636390 

29.9570466 

65 

36.1974182 

33.9803880 

31.9645236 

30.1285146 

66 

36.4680551 

34.2106499 

32.1605085 

30.2953934 

67 

36.7333853 

34.4358449 

32.3517133 

30.4578058 

68 

36.9935129 

34.6560846 

32.5382546 

30.6158715 

69 

37.2485400 

34.8714779 

32.7202461 

30.7697067 

70 

37.4985665 

35.0821315 

32.8977987 

30.9194247 

71 

37.7436905 

35.2881497 

33.0710207 

31.0651356 

72 

37.9840081 

35.4896346 

33.2400178 

31.2069467 

73 

38.2196136 

35.6866858 

33.4048930 

31.3449624 

74 

38.4505993 

35.8794009 

33.5657468 

31.4792843 

75 

38.6770560 

36.0678754 

33.7226774 

31.6100112 


198 





TABLE VI 


Rate, 2% to 2%?^ 
Years, 76 to. 100 


ACTUAL VALUE OF AN ANNUITY 


The actual value of an annuity or an annual instalment of $1 payable for 
one to one hundred years at a fixed rate of compound discount. 


Years 2% 2Vi<fo 2^/2% 2%% 


76 

38.8990723 

36.2522025 

77 

39.1167353 

36.4324735 

78 

39.3301303 

36.6087777 

79 

39.5393412 

36.7812023 

80 

39.7444499 

36.9498328 

81 

39.9455368 

37.1147525 

82 

40.1426808 

37.2760432 

83 

40.3359593 

37.4337847 

84 

40.5254480 

37.5880552 

85 

40.7112212 

37.7389310 

86 

40.8933518 

37.8864867 

87 

41.0719112 

38.0306955 

88 

41.2469694 

38.1719288 

89 

41.4185951 

38.3099565 

90 

41.5868555 

38.4449469 

91 

41.7518167 

38.5769669 

92 

41.9135434 

38.7060818 

93 

42.0720990 

38.8323556 

94 

42.2275456 

38.9558507 

95 

42.3799442 

39.0766284 

96 

42.5293546 

39.1947483 

97 

42.6758354 

39.3102690 

98 

42.8194441 

39.4232477 

99 

42.9602368 

39.5337403 

100 

43.0982688 

39.6418016 


33.87S7804 

34.0251491 

34.1708747 

34.3130460 

34.4517497 

34.5870704 

34.7190906 

34.8478907 

34.9735494 

35.0961432 

35.2157469 

35.3324334 

35.4362739 

35.5573378 

35.6656928 

35.7714050 

35.8745388 

35.9751572 

36.07332144 

36.16909146 


31.7372393 

31.8610623 

31.9815713 

32.0988551 

32.2129999 

32.3240897 

32.4322063 

32.5374293 

32.6398361 

32.73950215 

32.83650069 

32.93090319 

33.02277905 

33.11219601 

33.19921981 

33.28391453 

33.36634245 

33.44656432 

33.52463917 

33.60062434 


36.26252568 33.67457589 
36.35368098 33.74654816 
36.44261294 33.81659418 
36.52937580 33.88476548 
36.61402250 33.95111226 


199 




Rate. 3X to 
Years, 1 to 25 


TABLE VI 


ACTUAL VALUE OF AN ANNUITY 


The actual value of an annuity or an annual instalment of $1 payable for 
one to one hundred years at a fixed rate of compound discount. 


Years 

3 fo 

31/4% 

31 / 2 % 

3%% 

1 

0.9708737 

0.9685229 

0.9661837 

0.9638552 

2 

1.9134697 

1.9065599 

1.8996944 

1.8928726 

3 

2.8286113 

2.8150701 

2.8016380 

2.7883106 

4 

3.7170983 

3.6949831 

3.6730808 

3.6513832 

5 

4.5797071 

4.5471987 

4.5150548 

4.4832608 

6 

5.4171923 

5.3725889 

5.3285562 

5.2850702 

7 

6.2302845 

6.1719986 

6.1145479 

6.0578987 

8 

7.0196942 

6.9462453 

6.8739608 

6.8027937 

9 

. 7.7861117 

7.6961212 

7.6076925 

7.5207647 

10 

8.5302064 

8.4223929 

8.3166122 

8.2127853 

11 

9.2526282 

9.1258041 

9.0015591 

8.8797929 

12 

9.9540085 

9.8070734 

9.6633437 

9.5226915 

13 

.10.6349605 

10.4668984 

10.3027943 

10.1423528 

14 

11.2960790 

11.1059541 

10.9205324 

10.7396166 

15 

11.9379414 

11.7248939 

11.5174243 

11.3152931 

16 

12.5611090 

12.3243515 

12.0941314 

11.8701620 

17 

13.1661260 

12.9049398 

12.6513363 

12.4049751 

18 

13.7535213 

13.4672533 

13.1896987 

12.9204577 

19 

14.3238080 

14.0118667 

13.7098554 

13.4173084 

20 

14.8774844 

14.5393371 

14.2124225 

13.8962010 

21 

15.4150343 

15.0502042 

14.6979947 

14.3577841 

22 

15.9369274 

15.5449909 

15.1671467 

14.8026836 

23 

16.4436199 

16.0242031 

15.6204334 

15.2315023 

24 

16.9355544 

16.4883312 

16.0583918 

15.6448215 

25 

17.4131608 

16.9378496 

16.4815400 

16.0432016 


200 





TABLE VI 


Rate, 3% to 3%%’ 
Years, 26 to 50 


ACTUAL VALUE OF AN ANNUITY 


The actual value of an annuity or an annual instalment of $1 payable for 
one to one hundred years at a fixed rate of compound discount. 


Years 3% 3%% 3%% 


26 

27 

28 

29 

30 


17.8768564 

18.3270463 

18.7641238 

19.1884710 

19.6004587 


17.3732184 

17.7948832 

18.2032752 

18.5988123 

18.9818990 


16.8903787 

17.2853921 

17.6670477 

18.0357972 

18.3920769 


16.4271824 

16.7972844 

17.1540091 

17.4978402 

17.8292437 


31 

32 

33 

34 

35 


20.0004467 

20.3887847 

20.7658118 

21.1318576 

21.4872418 


19.3529273 

19.7122767 

20.0603149 

20.3973978 

20.7238702 


18.7363084 

19.0688992 

19.3902432 

19.7007204 

20.0006985 


18.1486687 

18.4565482 

18.7532995 

19.0393248 

19.3150119 


36 

37 

38 

39 

40 


21.8322749 

22.1672586 

22.4924855 

22.8082397 

23.1147973 


21.0400662 

21.3463093 

21.6429128 

21.9301800 

22.2084049 


20.2905324 

20.5705652 

20.8411283 

21.1025419 

21.3551155 


19.5807345 

19.8368526 

20.0837135 

20.3216517 

20.5509897 


41 

42 

43 

44 

45 


23.4124260 

23.7013860 

23.9819296 

24.2543021 

24.5187414 


22.4778721 

22.7388572 

22.9916273 

23.2364409 

23.4735485 


21.5991480 

21.8349282 

22.0627352 

22.2828386 

22.4954989 


20.7720384 

20.9850974 

21.1904554 

21.3383909 

21.5591721 


46 

47 

48 

49 

50 


24.7754786 

25.0247380 

25.2667374 

25.5016884 

25.7297961 


23.7031928 

23.9256085 

24.1410233 

24.3496574 

24.5517242 


22.7009679 

22.8994886 

23.0912961 

23.2766174 

23.4556718 


21.7630576 

21.9402966 

22.1111294 

22.2757875 

22.4344941 


201 





Rate, 3% to 33 / 4 % 
Year#, 51 to 75 


TABLE VI 


ACTUAL VALUE OF AN ANNUITY 


The actual value of an annuity or an annual instalment of $1 payable for 
•one to one hundred years at a fixed rate of compound discount. 


Years 




24.7474306 

24.9369767 

25.1205565 

25.2983577 

25.4705622 

25.6373462 

25.7988803 

25.9553298 

26.1068548 

26.2536102 

26.3957461 

26.5334080 

26.6667367 

26.7958686 

26.9209358 

27.0420663 

27.1593839 

27.2730087 

27.3830570 

27.4896412 


3 %% 


23.6286712 

23.7958204 

23.9573173 

24.1633529 

24.2641120 

24.4097730 

24.5505082 

24.6864843 

24.8178622 

24.9447974 

25.0674401 

25.1859355 

25.3004238 

25.4110405 

25.5179166 


3%% 


22.5874643 

22.7349055 

22.8770175 

23.0139929 

23.1460174 

23.2732699 

23.3959229 

23.5141427 

23.6280895 

23.7379177 

23.8437762 

23.9458085 

24.04415289 

24.13894268 

24.23030634 


51 25.9512599 

52 26.1662732 

53 26.3750241 

54 26.5776949 

55 26.7744626 

56 26.9654993 

57 27.1509718 

58 27.3310422 

59 27.5058678 

60 27.6756015 

61 27.8403915 

62 28.0003813 

63 28.1557117 

64 28.3065179 

65 28.4529317 

66 28.5950810 

67 28.7330900 

68 28.8670793 

69 28.9971661 

70 29.1234639 

71 29.2460832 

72 29.3651311 

73 29.4807116 

74 29.5929256 

75 29.7018713 


25.6211785 24.31836768 
25.72094842 24.40324608 
25.81734449 24.48505666 
25.91048089 24.56391020 
26.00046777 24.63991359 


27.5928705 26.08741159 24.71316984 
27.6928504 26.17141527 24.78377829 
27.78968329 26.25257829 24.85183462 
27.88346816 26.33099669 24.91743110 
27.97430092 26.40676326 24.98065664 


202 




TABLE VI 


Rate, 3% to 
Years, 76 to 100 


ACTUAL VALUE OF AN ANNUITY 


The actual value of an annuity or an annual instalment of $1 payable for 
one to one hundred years at a fixed rate of compound discount. 


Years 3% 3%% 3%'?^) 


76 29.8076438 

77 29.9103355 

78 30.0100362 

79 30.1068330 

80 30.20081057 

81 30.29205086 

82 30.38063368 

83 30.46663638 

84 30.55013418 

85 30.63120004 

86 30.70990474 

87 30.78631708 

88 30.86050380 

89 30.93252978 

90 31.00245796 

91 31.07034938 

92 31.13626339 

93 31.20025756 

94 31.26238783 

95 31.32270850 

96 31.38127225 

97 31.43813026 

98 31.49333222 

99 31.54692635 
100 31.59895952 


28.06227458 

28.14747908 

28.23000157 

28.30992651 

28.38733558 

28.46230805 

28.53492062 

28,60524755 

28.67336081 

28.73933004 

28.80322274 

28.86510427 

28.92503794 

28.98308505 

29.03930506 

29.09375542 

29.14649186 

29.19756830 

29.24703701 

29.29494858 

29.34135203 

29.38629483 

29.42982298 

29.47198099 

29.51281200 

203 


26.47996768 

26.55069658 

26.61903368 

26.68505988 

26.74885334 

26.81048955 

26.87004143 

26.92757948 

26.98317182 

27.03688425 

27.08878030 

27.13892139 

27.18736688 

27.23417412 

27.27939854 

27.32309361 

27.36531109 

27.40610093 

27.44551142 

27.48358919 

27.52037931 

27.55592533 

27.59026931 

27.62345189 

27.65551237 


25.04159692 

25.10033456 

25.15694916 

25.21151742 

25.26411333 

25.31480819 

25.36367069 

25.41076717 

25.45616127 

25.49991465 

25.54208657 

25.58273412 

25.62191258 

25.65967494 

25.69607239 

25.73115429 

25.76496816 

25.79755984 

25.82897351 

25.85925174 

25.88843558 

25.91656458 

25.94367687 

25.96980920 

25.99499697 




Rate, 4X to 4%^ 
Years, I to 25 


TABLE VI 


ACTUAL VALUE OF AN ANNUITY 


The actual value of an annuity or an annual instalment of $1 payable for 
one to one hundred years at a fixed rate of compound discount. 


Years 

4% 

4%% 

4%% 

4%% 

1 

0.9615384 

0.9592324 

0.9569377 

0.9546540 

2 

1.8860946 

1.8793598 

1.8726677 

1.8660182 

3 

2.7750910 

2.7619762 

2.7489643 

2.7360554 

4 

3.6298958 

3.6086102 

3.5875263 

3.5666400 

5 

4.4518236 

4.4207290 

4.3899782 

4.3595884 

6 

5.2421388 

5.1997400 

5.1578739 

5.1165536 

7 

6.0020575 

5.9469924 

5.8927024 

5.8391936 

8 

6.7327483 

6.6637814 

6.5958874 

6.5290648 

9 

7.4353360 

7.3513487 

7.2687919 

7.1876528 

10 

8.1109008 

8.0108853 

7.9127196 

7.8163767 

11 

8.7604825 

8.6435344 

8.5289183 

8.4165904 

12 

9.3850804 

9.2503920 

9.1185823 

8.9895871 

13 

9.9856553 

9.8325095 

9.6828538 

9.5366005 

14 

10.5631311 

10.3908958 

10.2228267 

10.0588090 

15 

11.1183965 

10.9265179 

10.7395469 

10.5573376 

16 

11.6523055 

11.4403041 

11.2340162 

11.0332599 

17 

12.1656795 

11.9331445 

11.7071925 

11.4876009 

18 

12.6593086 

12.4058934 

12.1599928 

11.9213395 

19 

13.1339518 

12.8593691 

12.5932946 

12.3354096 

20 

13.5903396 

13.2943578 

13.0079373 

12.7307034 

21 

14.0291739 

13.7116131 

13.4047247 

13.1080723 

22 

14.4511302 

14.1118580 

13.7844254 

13.4683290 

23 

14.8568572 

14.4957861 

14.1477754 

13.8122495 

24 

15.2469796 

14.8640624 

14.4954786 

14.1405748 

25 

15.6220973 

15.2173247 

14.8282090 

14.4540116 


204 




TABLE VI 


Rate, 4% to 4%% 
Years, 26.to 50 


ACTUAL VALUE OF AN ANNUITY 


The actual value of an annuity or an annual instalment of $1 payable for 
one to one hundred years at a fixed rate of compound discount. 


Years 4% 

4%% 


■ 

26 

15.9827874 

15.5561856 

15.1466113 

14.7532362 

27 

16.3296047 

15.8812320 

15.4513026 

15.0388913 

28 

16.6630829 

16.1930270 

15.7428732 

15.3115931 

29 

16.9837350 

16.4921119 

16.0218881 

15.5719289 

30 

17.2920546 

16.7790030 

16.2888880 

15.8204596 

31 

17.5885157 

17.0541983 

16.5443903 

16.0577204 

32 

17.8735745 

17.3181745 

16.7888901 

16.2842224 

33 

18.1476696 

17.5713891 

17.0228611 

16.5004534 

34 

18.4112225 

17.8142808 

17.2467569 

16.7068793 

35 

18.6646388 

18.0472704 

17.4610112 

16.9039445 

36 

18.9083082 

18.2707616 

17.6660392 

17.0920735 

37 

19.1426059 

18.4851416 

17.8622383 

17.2716717 

38 

19.3678921 

18.6907819 

18.0499886 

17.4431259 

39 

19.5845134 

18.8880388 

18.2296540 

17.6068053 

40 

19.7928032 

19.0772540 

18.4015826 

17.7630625 

41 

19.9930818 

19.2587554 

18.5661076 

17.9122340 

42 

20.1856575 

19.4328575 

18.7235477 

18.0546412 

43 

20.3708264 

19.5998619 

18.8742081 

18.1905908 

44 

20.5488734 

19.7600579 

19.0183808 

18.3203756 

45 

20.7200725 

19.9137231 

19.1563451 

18.4442752 

46 

20.8846870 

20.0811238 

19.2883683 

18.5625565 

47 

21.0429703 

20.2025153 

19.4147063 

18.6754742 

48 

21.1951658 

20.3381426 

19.5356039 

18.7832715 

49 

21.3415075 

20.4682408 

19.6512954 

18.8861806 

50 

21.4822208 

20.5930352 

19.7620049 

18.98442325 


205 




Rate, 4% to 4%% 
Yean. 51 to 75 


TABLE VI 


ACTUAL VALUE OF AN ANNUITY. 


The actual value of an annuity or an annual instalment of $1 payable for 
one to one hundred yeara at a fixed rate of compound discount. 


Years 4% 


41/4% 


20.7127420 

20.8275687 

20.9377142 

21.0433693 

21.1447171 

21.24193322 

21.33518609 

21.42463727 

21.51044177 

21.59274825 

2L67169934 

21.74743179 

21.82007681 

21.88976026 

21.95660287 

22.02072051 

22.08222422 

22.14122057 

22.19781181 

22.25209595 

22.30416706 

22.35411536 

22.40202739 

22.44798619 

22.49207136 


4 %% 


19.8679470 

19.9693270 

20.0663410 

20.1591777 

20.2480166 

20.33303002 

20.41438256 

20.49223188 

20.56672882 

20.63801777 

20.70623683 

20.77151822 

20.83398848 

20.89376865 

20.95097453 

21.00571701 

21.05810217 

21.10823148 

21.15620210 

21.20210699 

21.24603512 

21.28807161 

21.32829792 

21.36679199 

21.40362842 


4% 


19.07821094 

19.16774576 

19.25322052 

19.33481936 

19.41271803 

19.48708428 

19.55807836 

19.62585314 

19.69055460 

19.75232209 

19.81128867 

19.86758135 

19.92132139 

19.97264454 

20.02160130 

20.06835717 

20.11299283 

20.15560444 

20.19628378 

20.23511848 

20.27219220 

20.30758475 

20.34137241 

20.37362792 

20.40442078 


51 21.6175221 

52 21.7476194 

53 21.8727130 

54 21.9929954 

55 22.1086515 

56 22.2198593 

57 22.3267898 

58 22.4296076 

59 22.52847097 

60 22.62353189 

61 22.71493663 

62 22.80282583 

63 22.88733467 

64 22.96859321 

65 23.04672641 

66 23.12185450 

67 23.19409308 

68 23.26355326 

69 23.33034189 

70 23.39456173 

71 23.45631157 

72 23.51568645 

73 23.57277768 

74 23.62767308 

75 23.68045712 


206 





TABLE VI 


Rale. *% to VAX 
Years, u 76 to 100 


ACTUAL VALUE OF AN ANNUITY 


The actual value of an annuity or an annual instalment of $1 payable for 
one to one hundred years at a fixed rate of compound discount. 


Years 4%^^ 4%^^ 


76 23.73121102 22.53435929 

77 23.78001284 22.57492325 

78 23.82693768 22.61383352 

79 23.87205770 22.65115752 

80 23.91544234 22.68695992 

81 23.95715832 22.72130275 

82 23.99726986 22.75424552 

83 24.03583865 22.78584529 

84 24.07292404 22.81615681 

85 24.10858306 22.84523260 

86 24.14287058 22.87312305 

87 24.17583937 22.89987647 

88 24.20754011 22.92553923 

89 24.23802161 22.95015579 

90 24.26733075 22.97376878 

91 24.29551262 22.99641914 

92 24.32261058 23.01814610 

93 24.34866630 23.03898731 

94 24.37371989 23.05897887 

95 24.39780988 23.07815542 

96 24.42097333 23.09655019 

97 24.44324588 23.11419505 

98 24.46466179 23.13112058 

99 24.48525402 23.14735610 
100 24.50505424 23.16292974 

207 


21.43887859 20.43381731 
21.47261081 20.46188082 
21.50489044 20.48867176 
21.53578004 20.51424783 
21.56533947 20.53866414 

21.59362600 20.56197327 
21.62069444 20.58422542 
21.64659726 20.60546852 
21.67138465 20.62574833 
21.69510464 20.64510853 

21.71780319 20.66359083 
21.73952429 20.68123503 
21.76031004 20.69807914 
21.78020070 20.71415944 
21.79923483 20.72951056 

21.81744930 20.74416557 
21.83487942 20.75815603 
21.85155896 20.77151208 
21.86752024 20.78426249 
21.88279419 20.79643472 

21.89741042 20.80805498 
21.91139724 20.81914831 
21.92478175 20.82973860 
21.93758989 20.83984867 
21.94984649 20.849500284 




RaU/ S% to SViX^ 
Years, 1 to 25 


TABLE VI 


ACTUAL VALUE OF AN ANNUITY 


The actual value of an annuity or an annual instalment of $1 payable for 
one to one hundred years at a fixed rate of compound discount. 


Years 

5fo 

51 / 4 % 


1 

0.9523809 

0.9501187 

0.9478672 

2 

1.8594103 

1.8528443 

1.8463194 

3 

2.7232479 

2.7105409 

2.6979328 

4 

3.5459503 

3.5254546 

3.5051494 

5 

4.3294765 

4.2997195 

4.2702834 

6 

5.0756918 

5.0353630 

4.9955289 

7 

5.7863731 

5.7343116 

5.6829652 

8 

6.4632124 

6.3983959 

6.3345635 

9 

7.1078214 

7.0293549 

6.9521922 

10 

7.7217347 

7.6288409 

7.5376222 

11 

8.3064140 

8.1984238 

8.0925321 

12 

8.8632514 

8.7395952 

8.6185131 

13 

9.3935728 

9.2537722 

9.1170732 

14 

9.8986407 

9.7423015 

9.5896420 

15 

10.3796578 

10.2064624 

10.0375744 

16 

10.8377692 

10.6474704 

10.4621549 

17 

11.2740659 

11.0664803 

10.8646008 

18 

11.6895866 

11.4645895 

11.2460661 

19 

12.0853205 

11.8428405 

11.6076445 

20 

12.4622099 

12.2022239 

11.9503728 

21 

12.8211522 

12.5436808 

12.2752338 

22 

13.1630021 

12.8681054 

12.5831588 

23 

13.4885734 

13.1763473 

12.8750308 

24 

13.7986413 

13.4692137 

13.1516867 

25 

14.0939440 

13.7474716 

13.4139198 


208 




TABLE VI 


Rate, 5% to 5%% 
Year#, 2^ to 50 


ACTUAL VALUE OF AN ANNUITY 


The actual value of an annuity or an annual instalment of $1 payable for 
one to one hundred years at a fixed rate of compound discount. 


Years 

5% 

51 / 4 % 

5%% 

26 

14.3751847 

14.0118497 

13.6624820 

27 

14.6430330 

14.2630403 

13.8980859 

28 

14.8981266 

14.5017012 

14.1214071 

29 

15.1410729 

14.7284574 

14.3330860 

30 

15.3724503 

14.9439027 

14.5337295 

31 

15.5928098 

15.1486013 

14.7239128 

32 

15.8026759 

15.3430893 

14.9041813 

33 

16.0025485 

15.5278760 

15.0750520 

34 

16.1929033 

15.7034453 

15.2370147 

35 

16.3741936 

15.8702570 

15.3905338 

36 

16.5468510 

16.0287479 

15.5360495 

37 

16.7112866 

16.1793331 

15.6739791 

38 

16.8678920 

16.3224069 

15.8047180 

39 

17.0170399 

16.4583440 

15.9286412 

40 

17.1590856 

16.5875004 

16.0461039 

41 

17.2943672 

16.7102143 

16.1574430 

42 

17.4232068 

16.8268071 

16.2629776 

43 

17.5459112 

16.9375841 

16.3630104 

44 

17.6627725 

17.0428354 

16.45782822 

45 

17.7740690 

17.1428367 

16.54770294 

46 

17.8800657 

17.23784979 

16.63289224 

47 

17.9810086 

17.32812349 

16.71364038 

48 

18.07715099 

17.41389423 

16.79017888 

49 

18.16872089 

17.49538663 

16.86272723 

50 

18.25592461 

17.57281410 

16-93149342 


19 


209 




Rate. 5% to 51 / 2 ^ 
Year*, 51 to 75 


TABLE VI 


ACTUAL VALUE OF AN ANNUITY 


The actual value of an annuity or an annual instalment of $1 payable for 
one to one hundred years at a fixed rate of compound discount. 


Years 

5% 

5V4^o 


51 

18.33897577 

17.64637939 

16.99667465 

52 

18.41807211 

17.71627516 

17.05845779 

53 

18.49340196 

17.78268444 

17.11702000 

54 

18.56514468 

17.84578114 

17.17252920 

55 

18.63347107 

17.90573049 

17.22514455 

56 

18.69854383 

17.96268949 

17.27501692 

57 

18.76051789 

18.01680732 

17.32228930 

58 

18.88954079 

18.06822568 

17.36709724 

59 

18.87575309 

18.11707922 

17.40956922 

60 

18.92928860 

18.16345589 

17.44982702 

61 

18.98027481 

18.20759724 

17.48798606 

62 

19.02883310 

18.24949876 

17.52415577 

63 

19.07507909 

18.28931018 

17.55843985 

64 

19.11912289 

18.32713576 

17.59093660 

65 

19.16106937 

18.36307455 

17.62173921 

66 

19.20101840 

18.39722067 

17.65093599 

67 

19.23906509 

18.42966354 

17.67861067 

68 

19.27530003 

18.46048812 

17.70484259 

69 

19.30980950 

18.48977513 

17.72970696 

70 

19.34267566 

18.51760127 

17.75327508 

71 

19.37397676 

18.54403941 

17.77561453 

72 

19.40378734 

18.56915879 

17.79678936 

73 

19.43217837 

18.59302518 

17.81686029 

74 

19.45921744 

18.61570109 

17.83588486 

75 

19.48496893 

18.63724589 

17.85391763 


210 





TABLE VI 


Rate, 5%" to 5%% 
Years, 76 to 100 


ACTUAL VALUE OF AN ANNUITY 


The actual value of an annuity or an annual instalment of $1 payable for 
one to one hundred years at a fixed rate of compound discount. 


Years 

5% 

5%% 

5V2<fo 

76 

19.50949417 

18.65771601 

17.87101030 

77 

19.53285153 

18.67716505 

17.88721189 

78 

19.55509664 

18.69564395 

17.90256884 

79 

19.57628246 

18.71320110 

17.91712519 

80 

19.59645943 

18.72988248 

17.93092268 

81 

19.61567559 

18.74573177 

17.94400087 

82 

19.63397670 

18.76079048 

17.95639725 

83 

19.65140633 

18.77509805 

17.96814737 

84 

19.66800598 

18.78869194 

17.97928493 

85 

19.68381517 

18.80160775 

17.98984186 

86 

19.69887154 

18.81387930 

17.99984842 

87 

19.71321094 

18.82553873 

18.009333314 

88 

19.72686751 

18.83661657 

18.018323734 

89 

19.73987377 

18.84714184 

18.026845460 

90 

19.75226068 

18.85714209 

18.034922924 

91 

19.76405774 

18.866643519 

18.042579287 

92 

19.77529304 

18.875671005 

18.049836502 

93 

19.78599332 

18.884248189 

18.056715348 

94 

19.79618406 

18.892397533 

18.063235610 

95 

19.805889529 

18.900140377 

18.069415951 

96 

19.815132833 

18.907496999 

18.075274094 

97 

19.823935979 

18.914486664 

18.080826837 

98 

19.832319927 

18.921127674 

18.086090099 

99 

19.840304641 

18.927437423 

18.091078972 

100 

19.847909128 

18.933432434 

18.095807762 


211 






Rate, 5%X to 61 / 2 % 
Years, 1 to 25 


TABLE VI 


ACTUAL VALUE OF AN ANNUITY 


The actual value of an annuity or an annual instalment of $1. payable for 
one to one hundred years at a fixed rate of compound discount. 


Years 

5 ¥ 4 % 

6% 


1 

0.9456264 

0.9433960 

0.9389672 

2 

1.8398358 

1.8333924 

1.8206266 

3 

2.6854238 

2.6730114 

2.6484756 

4 

3.4850342 

3.4651047 

3.4257988 

5 

4.2411669 

4.2123627 

4.1556796 

6 

4.9561859 

4.9173229 

4.8410138 

7 

5.6323268 

5.5823797 

5.4845201 

8 

6.2717035 

6.2097917 

6.0887514 

9 

6.8763151 

6.8016898 

6.6561047 

10 

7.4480516 

7.3600842 

7.1888308 

11 

7.9887008 

7.8868713 

7.6890431 

12 

8.4999530 

8.3838402 

8.1587261 

13 

8.9834066 

8.8526787 

8.5997431 

14 

9.4405731 

9.2949792 

9.0138435 

15 

9.8728818 

9.7122437 

9.4026701 

16 

10.2816844 

10.1058894 

9.7677655 

17 

10.6682589 

10.4772533 

10.1105781 

18 

11.0338139 

10.8275966 

10.4324678 

19 

11.3794924 

11.1581091 

10.7347118 

20 

11.7063752 

11.4699133 

11.0185089 

21 

12.0154842 

11.7640682 

11.2849851 

22 

12.3077858 

12.0415728 

11.5351974 

23 

12.5841939 

12.3033696 

11.7701386 

24 

12.8455727 

12.5503476 

11.9907407 

25 

13.0927394 

12,7833458 

212 

12.1978788, 




TABLE VI 


Rale, 5%% to 6> 
Years, 26 to 50 


ACTUAL VALUE OF AN ANNUITY 


The actual value of an annuity or an annual instalment of $1 payable for 
one to one hundred years at a fixed rate of compound discount. 


Years 

5%% 

6 % 

6 % <70 

26 

13.3264668 

13.0031554 

12.3923747 

27 

13.5474856 

13.2105229 

12.5750000 

28 

13.7564868 

13.4061526 

12.7464791 

29 

13.9541239 

13.5907089 

12.9074923 

30 

14.1410147 

13.7648186 

13.0586784 

31 

14.3177436 

13.9290730 

13.2006372 

32 

14.4848631 

14.0840300 

13.3339319 

33 

14.6428958 

14.2302158 

13.4590912 

34 

14.7923356 

14.3681270 

13.5766117 

35 

14.9336499 

14.4982318 

13.6869596 

36 

15.0672804 

14.6209722 

13.7905726 

37 

15.1936449 

14.7367650 

13.88786184 

38 

15.3131385 

14.8460035 

13.97921324 

39 

15.4261349 

14.9490587 

14.06498920 

40 

15.5329872 

15.04628057 

14.14553002 

41 

15.6340296 

15.13799931 

14.22115519 

42 

15.72957794 

15.22452643 

14.29216474 

43 

15.81993098 

15.30615577 

14.35884039 

44 

15.90537122 

15.38316457 

14.42144662 

45 

15.98616576 

15.45581438 

14.48023182 

46 

16.06256721 

15.52435193 

14.53542920 

47 

16.13481444 

15.58900999 

14.58725771 

48 

16.20313333 

15.65000816 

14.63592299 

49 

16.26773747 

15.70755360 

14.68161808 

50 

16.32882887 

15.76184175 

14.72452428 


213 





Rate. to 6 ^ 2 % 

Year*, 51 to 75 


TABLE VI 


ACTUAL VALUE OF AN ANNUITY 


The actual value of an annuity or an annual instalment of $1 payable for 
one to one hundred years at a fixed rate of compound discount. 


Years 

5%% 

6 % 


51 

16.38659850 

15.81305697 

14.76481179 

52 

16.44122699 

15.86137321 

14.80264043 

53 

16.49288514 

15.90695457 

14.83816029 

54 

16.54173444 

15.94995585 

14.87151227 

55 

16.58792763 

15.99052310 

14.90282868 

56 

16.63160913 

16.02879408 

14.93223376 

57 

16.67291552 

16.06489878 

14.95984417 

58 

16.71197593 

16.09895981 

14.98576944 

59 

16.74891248 

16.13109285 

15.01011241 

60 

16.78384066 

16.16140705 

15.03296966 

61 

16.81686968 

16.19000534 

15.05443187 

62 

16.84810279 

16.21698486 

15.07458417 

63 

16.87763764 

16.24243724 

15.09350653 

64 

16.90556658 

16.26644891 

15.11127400 

65 

16.93197692 

16.28910143 

15.12795707 

66 

16.95695124 

16-31047173 

15.14362192 

67 

16.98056762 

16.33063239 

15.15833070 

68 

17.00289989 

16.34965188 

15.17214177 

69 

17.02401787 

16.36759479 

15.18510991 

70 

17.04398759 

16.38452206 

15.19728657 

71 

17.06287149 

16.40049119 

15.20872005 

72 

17.08072860 

16.41555640 

15.21945571 

73 

17.09761475 

16.42976886 

15.22953615 

74 

17.11358275 

16.44317684 

15.239001347 

75 

17.12868251 

16.45582588 

15.247888855 


214 





TABLE VI 


Rate, 5%%to6y25^ 
Years, 76 to 100 


ACTUAL VALUE OF AN ANNUITY 


The actual value of an annuity or an annual instalment of $1 payable for 
one to one hundred years at a fixed rate of compound discount. 


Years 5%% 

6 % 


76 

17.14296124 

16.46775893 

15.256233935 

77 

17.15646358 

16.47901653 

15.264069689 

78 

17.16923175 

16.48963690 

15.271427204 

79 

17.18130567 

16.49965612 

15.278335669 

80 

17.19272309 

16.509108214 

15.284822492 

81 

17.20351971 

16.518025282 

15.290913405 

82 

17.21372928 

16.526437610 

15.296632572 

83 

17.223383712 

16.534373767 

15.302002682 

84 

17.232513200 

16.541860709 

15.307045039 

85 

17.241146284 

16.548923859 

15.311779647 

86 

17.249309958 

16.555587208 

15.316225288 

87 

17.257029743 

16.561873387 

15.320399599 

88 

17.264329775 

16.567803742 

15.324319140 

89 

17.271232878 

16.573398417 

15.327999460 

90 

17.277760636 

16.578676412 

15.331455160 

91 

17.283933456 

16.583655652 

15.334699949 

92 

17.289770637 

16.588353049 

15.337746699 

93 

17.295290431 

16.592784554 

15.340607497 

94 

17.300510093 

16.596965220 

15.343293693 

95 

17.305445943 

16.600909244 

15.345815942 

96 

17.310113414 

16.604630021 

15.348184251 

97 

17.314527098 

16.608140187 

15.350408016 

98 

17.318700794 

16.611451665 

15.352496058 

99 

17.322647551 

16.614575700 

15.354456611 

100 

17.326379709 

16.617522903 

15.356297603 


215 





Rate, 1% to 8% 
Years, 1 to 25 


TABLE VI 


ACTUAL VALUE OF AN ANNUITY 


The actual value of an annuity or an annual instalment of $1 payable for 
one to one hundred years at a fixed rate of compound discount. 


Years 

7fo 

71 / 2 % 

8% 

1 

0.9345794 

0.9302326 

0.9259256 

2 

1.8080180 

1.7955650 

1.7832642 

3 

2.6243158 

2.6005254 

2.5770962 

4 

3.3872108 

3.3493257 

3.3121257 

5 

4.1001968 

4.0458840 

3.9927085 

6 

4.7665388 

4.6938451 

4.6628778 

7 

5.3892884 

5.2965997 

5.2063678 

8 

5.9712973 

5.8573015 

5.7466362 

9 

6.5152308 

6.3788846 

6.2468847 

10 

7.0235798 

6.8640782 

6.7100777 

11 

7.4986723 

7.3154210 

7.1389601 

12 

7.9426839 

7.7352747 

7.5360734 

13 

8.3576481 

8.1258362 

7.9037708 

14 

8.7454651 

8.4891492 

8.2442313 

15 

9.1079109 

8.8271147 

8.5594725 

16 

9.4466452 

9.1415013 

8.8513625 

17 

9.7632193 

9.4339539 

9.1216310 

18 

10.0590829 

9.7060029 

9.3718796 

19 

10.3355910 

9.9590716 

9.6035912 

20 

10.5940098 

10.1944844 

9.8181390 

21 

10.8355226 

10.4134730 

10.0167943 

22 

11.0612355 

10.6171833 

10.2007344 

23 

11.2721821 

10.8066813 

10.3710493 

24 

11.4693285 

10.9829585 

10.5287483 

25 

11.6535775 

11.1469372 

10.6747658 


216 






TABLE VI 


Rale, 7% to 8% 
Years, 26 to 50 


ACTUAL VALUE OF AN ANNUITY 


^ -The actual value of an annuity or an annual instalment of $1 payable for 
one to one hundred years at a fixed rate of compound discount. 


Years 

l°lo 

7%% 

8 fo 

26 

11.8257728 

11.2994756 

10.8099672 

27 

11.9867029 

11.4413717 

10.9351537 

28 

12.1371049 

11.5733681 

11.0510671 

29 

12.2776675 

11.6961554 

11.1583943 

30 

12.4090344 

11.8103761 

11.25777132 

31 

12.5318072 

11.9166280 

11.34978706 

32 

12.6465481 

12.01546692 

11.43498682 

33 

12.7537826 

12.10741009 

11.51387547 

34 

12.8540018 

12.19293861 

11.58692052 

35 

12.94766456 

12.27250003 

11.65455482 

36 

13.03519986 

12.34651065 

11.71717916 

37 

13.11700854 

12.41535773 

11.77516465 

38 

13.19346524 

12.47940152 

11.82885492 

39 

13.26492010 

12.53897713 

11.87856813 

40 

13.33170035 

12.59439629 

11.92459887 

41 

13.39411179 

12.64594900 

11.96721993 

42 

13.45244023 

12.69390500 

12.00668387 

43 

13.50695279 

12.73851523 

12.04322455 

44 

13.55789910 

12.78001312 

12.07705851 

45 

13.60551259 

12.81861580 

12.10838625 

46 

13.65001107 

12.85452527 

12.13739341 

47 

13.69159844 

12.88792942 

12.16425189 

48 

13.73046514 

12.91900305 

12.18912085 

49 

13.76678915 

12.94790875 

12.21214766 

50 

13.80073682 

12.97479777 

12.23346878 


217 





R&tei 7^ to 8^ 
Years, 51 to 75 


TABLE VI 


ACTUAL VALUE OF AN ANNUITY 


The actual value of an annuity or an annual instalment of $1 payable for 
one to one hundred years at a fixed rate of compound discount. 


Years 7% 


71/2^0 


12.99981081 

13.02307875 

13.04472335 

13.06485785 

13.08358762 

13.10101066 

13.11721814 

13.13229486 

13.14631972 

13.15936610 

13.17150226 

13.18279171 

13.19329353 

13.203062662 

13.212150226 

13.220603774 

13.228467538 

13.235782667 

13.242587437 

13.248917456 

13.254805845 

13.260283416 

13.265378830 

13.270118750 

13.274527977 


8^0 


12.25321056 

12.27148998 

12.28841527 

12.30408692 

12.31859771 

12.33203362 

12.34447428 

12.35599341 

12.36665927 

12.376535062 

12.385679314 

12.394146214 

12.401985936 

12.409244936 

12.415966231 

12.422189652 

12.427952079 

12.433287659 

12.438228010 

12.442802408 

12.447037962 

12.450959771 

12.454591075 

12.457953393 

12.461066650 


51 13.83246362 

52 13.86211483 

53 13.88982624 

54 13.91572475 

55 13.93992897 

56 13.96254973 

57 13.98369063 

58 14.00344848 

59 14.02191376 

60 14.03917103 

61 14.05529932 

62 14.07037248 

63 14.08445955 

64 14.09762503 

65 14.10992922 

66 14.12142846 

67 14.13217541 

68 14.14221929 

69 14.151606094 

70 14.160378808 

71 14.168577606 

72 14.176240035 

73 14.183401183 

74 14.190093843 

75 14.196348666 


218 





TABLE VI 


Rate, 1% to S% 
Years, 76 to 100 


ACTUAL VALUE OF AN ANNUITY 


The actual value of an annuity or an annual instalment of $1 payable for 
one to one hundred years at a fixed rate of compound discount. 


Years 

7% 

7%% 

Mo 

76 

14.202194294 

13.278629584 

12.463949302 

77 

14.207657498 

13.282445031 

12.466618418 

78 

14.212763295 

13.285994284 

12.469089821 

79 

14.217535068 

13.289295915 

12.471378157 

80 

14.221994669 

13.292367199 

12.473496986 

81 

14.226162520 

13.295224208 

12.475458865 

82 

14.230057707 

13.297881890 

12.477275419 

83 

14.233698070 

13.300354152 

12.478957414 

84 

14.237100278 

13.302653930 

12.480514816 

85 

14.240279911 

13.304793258 

12.481956855 

86 

14.243251531 

13.306783331 

12.483292076 

87 

14.246028745 

13.308634561 

12.484528392 

88 

14.248624272 

13.310356636 

12.485673129 

89 

14.251049998 

13.311958566 

12.486733070 

90 

14.253317032 

13.313448733 

12.4877144970 

91 

14.255435755 

13.314834935 

12.4886232256 

92 

14.257415870 

13.316124425 

12.4894646408 

93 

14.259266444 

13.317323950 

12.4902437290 

94 

14.260995953 

13.318439787 

12.4909651068 

95 

14.262612296 

13.319477775 

12.4916330491 

96 

14.264122916 

13.3204433454 

12.4922515142 

97 

14.265534710 

13.3213415504 

12.4928241670 

98 

14.266854144 

13.3221770900 

12.4933544000 

99 

14.268087260 

13.3229543360 

12.4938453573 

100 

14.269239705 

13.3236773555 

12.4942999474 


219 




Rate, 81/2% to 9y2% 
Years, ,1 to 25 


TABLE VI 


ACTUAL VALUE OF AN ANNUITY 


The actual value of an annuity or an annual instalment of $1 payable for 
one to one hundred years at a fixed rate of compound discount. ) 


Years 

81/2% 

9% 

91 / 2 % 

1 

0.9216592 

0.9174312 

0.9132420 

2 

1.7711146 

1.7591112 

1.7472530 

3 

2.5540230 

2.5312947 

2.5089070 

4 

3.2755975 

3.2397199 

3.2044812 

5 

3.9406431 

3.8896512 

3.8397089 

6 

4.5535885 

4.4859185 

4.4198257 

7 

5.1185152 

5.0329527 

4.9496127 

8 

5.6391849 

5.5348189 

5.4334365 

9 

6.1190649 

5.9952466 

5.8752847 

10 

6.5613507 

6.4176574 

6.2787991 

11 

6.9689874 

6.8051903 

6.6473054 

12 

7.3446895 

7.1607250 

6.9838408 

13 

7.6909587 

7.4869037 

7.2911791 

14 

8.0101009 

7.7861501 

7.5718534 

15 

8.3042412 

8.0606882 

7.8281769 

16 

8.5753382 

8.3125580 

8.0622623 

17 

8.8251973 

8.5436312 

8.2760389 

18 

9.0554821 

8.7556249 

8.4712687 

19 

9.2677262 

8.9501145 

8.6495608 

20 

9.4633429 

9.1285454 

8.8123846 

21 

9.6436346 

9.2922434 

8.9610822 

22 

9.8098023 

9.4424251 

9.0968791 

23 

9.9629523 

9.5802064 

9.2208945 

24 

10.1041044 

9.7066113 

9.3341506 

25 

10.2341985 

9.8225791 

220 

9.4375808 




TABLE VI 


Rate, SVo^toBViX 
Years, 26 to 50 


ACTUAL VALUE OF AN ANNUITY 


The actual value of an annuity or an annual instalment of $1 payable for 
one to one hundred years at a fixed rate of compound discount. 


Years 

8 %% 

9% 

9Y2% 

26 

10.3541009 

9.9289716 

9.53203762 

27 

10.4646100 

10.02657940 

9.61829958 

28 

10.5664617 

10.11612784 

9.69707762 

29 

10.66033427 

10.19828236 

9.76902105 

30 

10.74685277 

10.27365348 

9.83472281 

31 

10.82659332 

10.34280131 

9.89472442 

32 

10.90008694 

10.40623968 

9.94952041 

33 

10.96782300 

10.46444002 

9.99956241 

34 

11.03025254 

10.51783482 

10.04526287 

35 

11.08779129 

10.56682088 

10.08699846 

36 

11.14082241 

10.61176222 

10.12511315 

37 

11.18969902 

10.65299281 

10.15992108 

38 

11.23474659 

10.69081904 

10.19170915 

39 

11.27626509 

10.72552200 

10.22073936 

40 

11.31453099 

10.75735957 

10.24725097 

41 

11.34979911 

10.78656836 

10.27146248 

42 

11.38230429 

10.81336541 

10.29357345 

43 

11.41226298 

10.83794986 

10.31376612 

44 

11.43987468 

10.86050440 

10.33220691 

45 

11.46532326 

10.88119664 

10.34904782 

46 

11.48877817 

10.90018035 

10.36442764 

47 

11.51039561 

10.91759659 

10.37847314 

48 

11.53031951 

10.93357480 

10.39130008 

49 

11.54868256 

10.94823370 

10.40301418 

50 

11.56560703 

10.96168224 

10.41371199 


221 





Rate. a^Xto 9 V 2 X 
Years, 51 to 75 


TABLE VI 


ACTUAL VALUE OF AN ANNUITY 


The actual value of an annuity or an annual instalment of $1 payable for 
one to one hundred years at a fixed rate of compound discount. 


Years 

8 %% 

9% 


51 

11.58120562 

10.97402034 

10.423481682 

52 

11.59558220 

10.98533970 

10.432403776 

53 

11.60883251 

10.99572444 

10.440551808 

54 

11.62104477 

11.005251722 

10.447992933 

55 

11.63230031 

11.013992348 

10.454788481 

56 

11.64267408 

11.022011270 

10.460994461 

57 

11.652235162 

11.029368080 

10.466662024 

58 

11.661047222 

11.036117446 

10.471837880 

59 

11.669168938 

11.042309524 

10.476564690 

60 

11.676654390 

11.047990331 

10.480881411 

61 

11.683553425 

11.053202070 

10.484823622 

62 

11.689911982 

11.057983491 

10.488423815 

63 

11.695772403 

11.062370116 

10.491711663 

64 

11.701173714 

11.066394542 

10.494714264 

65 

11.706151882 

11.070086676 

10.497456365 

66 

11.710740055 

11.073473956 

10.499960567 

67 

11.714968786 

11.076581552 

10.502247410 

68 

11.718866235 

11.079432557 

10.504335942 

69 

11.722458354 

11.082048158 

10.506243278 

70 

11.725769063 

11.084447792 

10.507985138 

71 

11.728820408 

11.086649291 

10.509575877 

72 

11.731632708 

11.088669015 

10.511028607 

73 

11.734224690 

11.090521973 

10.512355301 

74 

11.736613613 

11.092221934 

10.513566893 

75 

11.738815386 

11.093781532 

10.514673370 


222 





TABLE VI 


Rale, SVs^to SVsX 
Yean, 76 to 106 


ACTUAL VALUE OF AN ANNUITY 


The actual value of an annuity or an annual instalment of $1 payable for 
one to one hundred years at a fixed rate of compound discount. 


Years 9% 


76 11.740844670 

77 11.742714978 

78 11.744438764 

79 11.746027507 

80 11.747491786 


11.095212355 

11.096525037 

11.097729332 

11.098834190 

11.099847821 


10.515683852 

10.5166066662 

10.5174494190 

10.5182190564 

10.5189219216 


81 11.748841353 

82 11.750085193 

83 11.751231590 

84 11.752288177 

85 11.7532619899 


11.100777758 

11.1016309112 

11.1024136206 

11.1031317026 

11.1037904934 


10.5195638076 

10.5201500049 

10.5206853449 

10.5211742399 

10.5216207194 


86 11.7541595133 

87 11.7549867239 

88 11.7557491301 

89 11.7564518086 

90 11.7570994386 


11.1043948885 

11.1049493795 

11.1054580868 

11.1059247908 

11.1063529596 


10.5220284632 

10.5224008320 

10.5227408949 

10.5230514546 

10.5233350708 


91 11.7576963327 

92 11.7582464656 

93 11.7587535005 

94 11.7592208138 

95 11.7596515174 


11.1067457750 

11.1071061561 

11.1074367809 

11.1077401064 

11.1080183867 


10.5235940810 

10.5238306200 

10.5240466373 

10.5242439134 

10.5244240743 


96 11.7600484793 

97 11.7604143428 

98 11.7607515442 

99 11.7610623289 
100 11.7613487665 


11.1082736898 

11.1085079128 

11.1087227962 

11.1089199370 

11.1091008001 


10.5245886048 

10.5247388610 

10.5248760813 

10.5250013966 

10.5251158398 


223 








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TABLE VII 


ACTUAL VALUE OF A SEMI-ANNUITY 



The actual value of a semi-annuity, or a semi-annual instalment of $1. pay¬ 
able for one to one hundred semi-annual periods, at the following rates of com¬ 
pound discount. 


11 /2% 

2 % 

2 %% 

3% 

31 / 2 % 

4% 


5% 

51 / 2 % 

6 % 

6 %% 

7% 

8 % 

9% 

10 % 

11 % 


EXAMPLE. —What is the actual value of a semi-annuity of $1000, to be re¬ 
ceived every six months for 42% years, or for 85 semi-annual periods @ iy 2 % 
per annum compound discount; or what is the capital which will be amortized by 
a semi-annuity of $1000, payable every six months @ 1%% per annum compound 
interest for 42% years ? 

Table VII, page 229, shows that the actual value today of a semi-annuity 
or semi-annual instalment of $1, or the capital which will be amortized by a semi- 
annuity, or a semi-annual instalment of $1., payable every six months, for 
85 semi-annual periods, @ 1%% per annum compound interest is: 
$62.6840007; therefore for a semi-annuity of $1000 it will be: 
62.6840007 X 1000=$62684.0007. 


20 


225 





Rate. iy2%to2i/2% 
Years, 1 to 12 


TABLE VII 


ACTUAL VALUE OF A SEMI-ANNUITY 


The actual value of a semi-annuity, or a semi-annual Instalment of $1 payable 
for one to one hundred semi-annual periods, at a fixed rate of compound discount. 


Years 

Semi-Annual 

Instalments 

iy2% 

2% 

21/2% 


1 

0.9925557 

0.9900989 

0.9876542 

1 

2 

1.9777229 

1.9703951 

1.9631156 


3 

2.9555563 

2.9409853 

2.9265346 

2 

4 

3.9261105 

3.9019657 

3.8780592 


5 

4.8894394 

4.8534316 

4.8178366 

3 

6 

5.8455976 

5.7954768 

5.7460116 


7 

6.7946378 

6.7281950 

6.6627280 

4 

8 

7.7366138 

7.6516780 

7.5681266 


9 

8.6715776 

8.5660180 

8.4623474 

5 

10 

9.5995796 

9.4713050 

9.3455294 


11 

10.5206732 

10.3676284 

10.2178078 

6 

12 

11.4349104 

11.2550778 

11.0793176 


13 

12.3423416 

12.1337398 

11.9301912 

7 

14 

13.2430178 

13.0037020 

12.7705606 


15 

14.1369894 

13.8650506 

13.6005544 

8 

16 

15.0243056 

14.7178708 

14.4203018 


17 

15.9050168 

15.5622480 

15.2299285 

9 

18 

16.7791716 

16.3982560 

16.0295601 


19 

17.6468190 

17.2260042 

16.8193198 

10 

20 

17.5080076 

18.0455480 

17.5993297 


21 

19.3627852 

18.8569774 

18.3697097 

11 

22 

20.2112000 

19.6603730 

19.1305790 


23 

21.0532988 

20.4558140 

19.8820549 

12 

24 

21.8891284 

21.2433792 

20.6242531 


25 

22.7187362 

22.0231469 

21.3572884 


226 




TABLE VII 

ACTUAL VALUE OF A SEMI-ANNUITY 


Rate, 11 / 2 % to 21 / 0 % 
Years, 13 to 25 


The actual value of a semi-annuity, or a semi-annual instalment of $1 payable 
for one to one hundred semi-annual periods, at a fixed rate of compound discount. 


Semi-Annual 
1 Cdib Instalments 


13 

26 


27 

14 

28 


29 

15 

30 


31 

16 

32 


33 

17 

34 


35 

18 

36 


37 

19 

38 


39 

20 

40 


41 

21 

42 


43 

22 

44 


45 

23 

46 


47 

24 

48 


49 

25 

50 


11/2% 


23.5421678 

24.3594698 

25.1706874 

25.9758670 

26.7750512 

27.5682859 

28.3556156 

29.1370841 

29.9127355 

30.6826125 

31.4467582 

32.2052154 

32.9580266 

33.7052336 

34.4468786 

35.1830026 

35.9136464 

36.6388511 

37.3586573 

38.0731053 

38.7822346 

39.4860852 

40.1846962 

40.8781063 

41.5663543 


29fc 


22.7951939 

23.5595972 

24.3164322 

25.0657737 

25.8076954 

26.5422717 

27.2695745 

27.9896767 

28.7026490 

29.4085622 

30.1074860 

30.7994896 

31.4846416 

32.1630102 

32.8346618 

33.4996636 

34.1580812 

34.8099796 

35.4554236 

36.0944769 

36.7272029 

37.3536646 

37.9739235 

38.5880414 

39.1960787 


2 %% 


22.0812739 

22.7963215 

23.5025415 

24.2000430 

24.8889331 

25.5693186 

26.2413044 

26.9049942 

27.5604902 

28.2078936 

28.8473043 

29.4788212 

30.1025418 

30.7185621 

31.3269772 

31.9278809 

32.5213660 

33.1075243 

33.6864460 

34.2582209 

34.8229367 

35.3806807 

35.9315393 

36.4755972 

37.0129381 


227 




Rate,l’/2%to2Vi% 
tYcart, 26 to 37 


TABLE VII 


ACTUAL VALUE OF A SEMI-ANNUITY 


The actual value of a semi-annuity, or a semi-annual instalment of $1 payable 
for one to one hundred semi-annual periods, at a fixed rate of compound discount. 


V#»arc Semi-Annual 
1 caib Instalments 



31 

26 

52 


53 

27 

54 


55 

28 

56 


57 

29 

58 


59 

30 

60 


61 

31 

62 


63 

32 

64 


65 

33 

66 


67 

34 

68 


69 

35 

70 


71 

36 

72 


73 

37 

74 


75 


11/2% 


42.2494788 

42.9275179 

43.6005097 

44.2684918 

44.9315014 

45.5895754 

46.2427505 

46.8910635 

47.5345496 

48.1732452 

48.8071861 

49.4368081 

50.0613458 

50.6812345 

51.2965083 

51.9072021 

52.5133498 

53.1149649 

53.7121413 

54.3048521 

54.8931508 

55.4770701 

56.0566428 

56.6319009 

57.2028770 


2% 


39.7980955 

40.3941518 

40.9843068 

41.5686186 

42.1471449 

42.7199433 

43.2870701 

43.8485821 

44.4045346 

44.9549824 

45.4999801 

46.0395818 

46.5738409 

47.1028105 

47.6265426 

48.1450881 

48.6585003 

49.1668295 

49.6701256 

50.1684386 

50.6618178 

51.1503117 

51.6339691 

52.1128381 

52.5869656 


2 %% 


37.5436435 

38.0678006 

38.5854849 

39.0967781 

39.6017589 

40.1005054 

40.5930947 

41.0796027 

41.5601044 

42.0346741 

42.5033850 

42.9663093 

43.4235184 

43.8750831 

44.3210729 

44.7615567 

45.1966026 

45.6262776 

46.0506479 

46.4697791 

46.8837359 

47.2925882 

47.6963809 

49.0951943 

48.4890846 


228 





TABLE VII 


Rate,iy2% to 2 V 2 X 
Years 38 to .50 


ACTUAL VALUE OF A SEMLANNUITY 


The actual value of a semi-annuity, or a semi-annual instalment of $1 payable 
for one to one hundred semi-annual periods, at a fixed rate of compound discount. 


V^o***? Semi-Annual 
1 cars Instalments 


38 

76 


77 

39 

78 


79 

40 

80 


81 

41 

82 


83 

42 

84 


85 

43 

86 


87 

44 

88 


89 

45 

90 


91 

46 

92 


93 

47 

94 


95 

48 

96 


97 

49 

98 


99 

50 

100 




57.7696024 

58.3321090 

58.8904282 

59.4445908 

59.9946279 

60.5405706 

61.0824488 

61.6202932 

62.1541339 

62.6840007 

63.2099228 

63.7319298 

64.2500509 

64.7643147 

65.2747503 

65.7813862 

66.2842507 

66.7833716 

67.2787769 

67.7704945 

68.2585515 

68.7429753 

69.2237929 

69.7010312 

70.1747166 


2 % 


53.0563987 

53.5211838 

53.9813671 

54.4369941 

54.8881098 

55.3347591 

55.7769860 

56.2148344 

56.6483478 

57.0775688 

57.5025401 

57.9233038 

58.3399015 

58.7523744 

59.1607634 

59.5651089 

59.9654509 

60.3618294 

60.7542831 

61.1428511 

61.5275719 

61.9084837 

62.2856240 

62.6590301 

63.0287391 


21/2% 


48.8781119 

49.2623364 

49.6418174 

50.0166134 

50.3867824 

50.7523814 

51.1134667 

51.4700944 

51.8223193 

52.1701957 

52.5137763 

52.8531163 

53.1882669 

53.5192799 

53.8462063 

54.1690966 

54.4880007 

54.8029676 

55.1140461 

55.4212841 

55.7247291 

56.0244279 

56.3204266 

56.6127711 

56.9015066 


229 





Rate, 3X to 4% 
Years, 1 to 12 


TABLE VII 


ACTUAL VALUE OF A SEMI-ANNUITY 


The actual value of a semi-annuity, or a semi-annual instalment of $1 payable 
for one to one hundred semi-annual periods, at a fixed rate of compound discount. 


Years 

Semi-Annual 

Instalments 

3% 

3y2% 

4</c 


1 

0.9852219 

0.9828010 

0.9803920 

1 

2 

1.9558839 

1.9486990 

1.9415609 


3 

2.9122013 

2.8979844 

2.8838833 

2 

4 

3.8543862 

3.8309426 

3.8077287 


5 

4.7826466 

4.7478556 

4.7134601 

3 

6 

5.6971898 

5.6489982 

5.6014317 


7 

6.5982172 

6.5346420 

6.4719933 

4 

8 

7.4859296 

7.4050534 

7.3254833 


9 

8.3605234 

8.2604948 

8.1622383 

4 

10 

9.2221918 

9.1012238 

8.9825863 


11 

10.0711264 

9.9274927 

9.7868487 

6 

12 

10.9075154 

10.7395313 

10.5753417 


13 

11.7315433 

11.5376229 

11.3483742 

7 

14 

12.5433939 

12.3219883 

12.1062486 


15 

13.3432468 

13.0928635 

12.8492630 

8 

16 

14.1312793 

13.8504800 

13.5777085 


17 

14.9076658 

14.5950665 

14.2918708 

9 

18 

15.6725788 

15.3268467 

14.9920298 


19 

16.4261878 

16.0460413 

15.6784601 

10 

20 

17.1686599 

16.7528663 

16.3514307 


21 

17.9001594 

17.4475351 

17.0112057 

11 

22 

18.6208489 

18.1302563 

17.6580440 


23 

19.3308881 

18.8012351 

18.2921991 

12 

24 

20.0304337 

19.4606739 

18.9139200 


25 

20.7196415 

20.1087709 

19.5234501 


230 




TABLE VII 


Rate. 3% to 4% 
Years, 13 to 25 


ACTUAL VALUE OF A SEMI-ANNUITY 


The actual value of a semi-annuity, or a semi-annual instalment of $1 payable 
for one to one hundred semi-annual periods at a fixed rate of compound discount. 


Years StS' 3% 31 / 2 % 4% 


13 

26 


27 

14 

28 


29 

15 

30 


31 

16 

32 


33 

17 

34 


35 

18 

36 


37 

19 

38 


39 

20 

40 


41 

21 

42 


43 

22 

44 


45 

23 

46 


47 

24 

48 


49 

25 

50 


21.3986640 

22.0676516 

22.7267526 

23.3761135 

24.0158779 

24.6461875 

25.2671821 

25.8789997 

26.4817757 

27.0756440 

27.6607359 

28.2371812 

28.8051079 

29.3646414 

29.9159059 

30.4590238 

30.9941152 

31.5212989 

32.0406917 

32.5524089 

33.0565639 

33.5532685 

34.0426327 

34.5247648 

34.9997720 


20.7455745 

21.3715701 

21.9867989 

22.5914465 

23.1856949 

23.7697226 

24.3437057 

24.9078170 

25.4622265 

26.0071003 

26.5426029 

27.0688954 

27.5861364 

28.0944811 

28.5940829 

29.0850921 

29.5676564 

30.0419212 

30.5080292 

30.9661205 

31.4163331 

31.8588024 

32.2936617 

32.7210419 

33.1410716 


20.1210286 

20.7068897 

21.2812634 

21.8443749 

22.3964454 

22.9376908 

23.4683235 

23.9885517 

24.4985793 

24.9986058 

25.4888278 

25.9694376 

26.4406236 

26.9025706 

27.3554600 

27.7994691 

28.2347721 

28.6615399 

29.0799394 

29.4901350 

29.8922876 

30.2865548 

30.6730913 

31.0520485 

31.4235753 


231 





Rat^, 3% to 4% 
Year#, 26 to 37 


TABLE VII 


ACTUAL VALUE OF A SEMI-ANNUITY 


■' The actual value of a semi-annuity, or a semi-annual instalment of $1 payable 
fw one to one hundred semi-annual periods, at a fixed rate of compound discount. 


Semi-Annual 
1 cdib Instalments 



51 

26 

52 


53 

27 

54 


55 

28 

56 


57 

29 

58 


59 

30 

60 


61 

31 

62 


63 

32 

64 


65 

33 

66 


67 

34 

68 


69 

35 

70 


71 

36 

72 


73 

37 

74 


75 


3% 


35.4677593 

35.9288306 

36.3830880 

36.8306323 

37.2715682 

37.7059771 

38.1339715 

38.5556409 

38.9710788 

39.3803773 

39.7836269 

40.1809172 

40.5723364 

40.9579711 

41.3379069 

41.7122278 

42.0810170 

42.4443559 

42.8023254 

43.1550047 

43.5024719 

44.8448042 

44.1820774 

44.5143662 

44.8417446 


31/2% 


33.5538772 

33.9595829 

34.3583110 

34.7501814 

35.1353120 

35.5138187 

35.8858155 

36.2514143 

36.6107252 

36.9638564 

37.3109140 

37.6520026 

37.9872248 

38.3166816 

38.6404720 

38.9586935 

39.2714420 

39.5788115 

39.8808945 

40.1777820 

40.4695634 

40.7563265 

41.0381576 

41.3151414 

41.5873614 


4^0 


31.7878172 

32.1449169 

32.4950148 

32.8382481 

33.1747512 

33.5046561 

33.8280924 

34.1451868 

34.4560636 

34.7608447 

35.0596497 

35.3525958 

35.6397979 

35.9213686 

36.1974182 

36.4680551 

36.7333853 

36.9935129 

37.2485400 

37.4985665 

37.7436905 

37.9840081 

38.2196136 

38.4505993 

38.6770560 


232 





TABLE VII 

ACTUAL VALUE OF A SEMI-ANNUITY 


Rate, 3% to 4% 
Years, 38 to 50 


The actual value of a semi-annuity, or a semi-annual instalment of $1 payable 
for one to one hundred semi-annual periods, at a fixed rate of compound discount. 


Viaov-e Semi-Annual 
i caib Instalments 


38 

76 


77 

39 

78 


79 

40 

80 


81 

41 

82 


83 

42 

84 


85 

43 

86 


87 

44 

88 


89 

45 

90 


91 

46 

92 


93 

47 

94 


.95 

48 

96 


97 

49 

98 


99 

50 

100 


3% 


45.1642850 

45.4820588 

45.7951364 

46.1035874 

46.4074800 

46.7068815 

47.0018584 

47.2924761 

47.5787990 

47.8608905 

48.1388132 

48.4126283 

48.6823972 

48.9481794 

49.2100339 

49.4680186 

49.7221908 

49.9726068 

50.2193220 

50.4623913 

50.7018685 

50.9378066 

51.1702579 

51.3992740 

51.6249057 


m<^o 


41.8548995 

42.1178362 

42.3762507 

42.6302207 

42.8798227 

43.1251318 

43.3662217 

43.6031652 

43.8360335 

44.0648967 

44.2898237 

44.5108822 

44.7281387 

44.9416586 

45.1515062 

45.3577446 

45.5604360 

45.7596413 

45.9554204 

46.1478323 

46.3369350 

46.5227853 

46.7054392 

46.8849516 

47.0613766 


4fo 


38.8990723 

39.1167353 

39.3301303 

39.5393412 

39.7444499 

39.9455368 

40.1426808 

40.3359593 

40.5254480 

40.7112212 

40.8933518 

41.0719112 

41.2469694 

41.4185951 

41.5868555 

41.7518167 

41.9135434 

42.0720990 

42.2275456 

42.3799442 

42.5293546 

42.6758354 

42.8194441 

42.960236:8 

43.0982688 


233 




Ratc,4V2% 10 5^2% 
Years, 1 to 12 


TABLE VII 


ACTUAL VALUE OF A SEMI-ANNUITY 


The actual value of a semi-annuity, or a semi-annual instalment of $1 payable 
for one to one hundred semi-annual periods, at a fixed rate of compound discount. 


Semi-Annual 
1 ears instalments 



1 

1 

2 


3 

2 

4 


5 

3 

6 


7 

4 

8 


9 

5 

10 


11 

6 

12 


13 

7 

14 


15 

8 

16 


17 

9 

18 


19 

10 

20 


21 

11 

22 


23 

12 

24 


25 


4 %^ 


0.9779950 

1.9344697 

2.8698981 

3.7847425 

4.6794555 

5.5544801 

6.4102493 

7.2471885 

8.0657101 

8.8662205 

9.6491159 

10.4147839 

11.1636036 

11.8959458 

12.6121725 

13.3126392 

13.9976922 

14.6676708 

15.3229067 

15.9637236 

16.5904397 

17.2033650 

17.8028031 

18.3890506 

18.9623977 


5 % 


0.9756097 

1.9274239 

2.8560238 

3.7619744 

4.6458286 

5.5081262 

6.3493912 

7.1701376 

7.9708660 

8.7520642 

9.5142087 

10.2577639 

10.9831837 

11.6909102 

12.3813750 

13.0549993 

13.7121936 

14.3533590 

14.9788861 

15.5891561 

16.1845316 

16.7654054 

17.3321019 

17.8849763 

18.4243660 


5i/2?fc 


0.9732360 

1.9204244 

2.8422626 

3.7394286 

4.6125828 

5.4623680 

6.2894098 

7.0943167 

7.8776812 

8.6400795 

9.3820734 

10.1042082 

10.8070160 

11.4910138 

12.1567049 

12.8045796 

13.4351145 

14.0487741 

14.6460096 

15.2272610 

15.7929555 

16.3435098 

16.8793293 

17.4008082 

17.9083304 


234 




TABLE VII 


Rate,4V4%lo5%% 
Years, 13 to 25 


ACTUAL VALUE OF A SEMI-ANNUITY 


The actual value of a semi-annuity, or a semi-annual instalment of $1 payable 
for one to one hundred semi-annual periods, at a fixed rate of compound discount. 


Semi-Annual 
1 cars Instalments 


13 

26 


27 

14 

28 


29 

15 

30 


31 

16 

32 


33 

17 

34 


35 

18 

36 


37 

19 

38 


39 

20 

40 


41 

21 

42 


43 

22 

44 


45 

23 

46 


47 

24 

48 


49 

25 

50 


4V2% 


19.5231285 

20.0715205 

20.6078455 

21.1323685 

21.6453492 

21.1470420 

22.6376950 

23.1175513 

23.5868484 

24.0458187 

24.4946895 

24.9336834 

25.3630172 

25.7829035 

26.1935498 

26.5951600 

26.9879332 

27.3720631 

27.7477404 

28.1151508 

28.4744765 

28.8258953 

29.1695812 

29.5057044 

29.8344312 


5% 


18.9505997 

19.4639985 

19.9648756 

20.4535360 

20.9302777 

21.3953913 

21.8491608 

22.2918628 

22.7237671 

23.1451370 

23.5562295 

23.9572953 

24.3485791 

24.7303194 

24.1027489 

25.4660947 

25.8205784 

26.1664162 

26.5038187 

26.8329919 

27.1541365 

27.4674483 

27.7731184 

28.0713331 

28.3622742 


51/2^0 


18.4022693 

18.8829886 

19.3508419 

19.8061735 

20.2493186 

20.6806035 

21.1003455 

21.5088536 

21.9064283 

22.2933625 

22.6699406 

23.0364400 

23.3931304 

23.7402745 

24.0781277 

24.4069387 

24.7269494 

25.0383953 

25.3415057 

25.6365036 

25.9236063 

26.2030249 

26.4749652 

26.7396273 

26.9972061 


235 




Rale,4H^^toS'^.V 

Years, ; 26 to 37 


TABLE VII 

ACTUAL VALUE OF A SEMI-ANNUITY 


The actual value of a semi-annuity, or a semi-annual instalment of $1 payable 
for one to one hundred semi-annual periods, at a fixed rate of compound discount. 


Semi-Annual 
1 Cal d Instalments 



51 

26 

52 


53 

27 

54 


55 

28 

56 


57 

29 

58 


59 

30 

60 


61 

31 

62 


63 

32 

64 


65 

34 

66 


67 

34 

68 


69 

35 

70 


71 

36 

72 


73 

37 

74 


75 




30.1559242 

30.4703429 

30.7778429 

31.0785764 

31.3726923 

31.6603363 

31.9416506 

32.2167746 

32.4858446 

32.7489937 

33.0063524 

33.2580478 

33.5042047 

33.7449450 

33.9803880 

34.2106499 

34.4358449 

34.6560846 

34.8714779 

35.0821315 

35.2881497 

35.4896346 

35.6866858 

35.8794009 

36.0678754 


5^0 


28.6461192 

28.9230411 

29.1932088 

29.4567869 

29.7139363 

29.9648140 

30.2095724 

30.4483611 

30.6813257 

30.9086082 

31.1303472 

31.3466779 

31.5577323 

31.7636390 

31.9645236 

32.1605085 

32.3517133 

32.5382546 

32.7202461 

32.8977987 

33.0710207 

33.2400178 

33.4048930 

33.5657468 

33.7226774 




27.2478911 

27.4918677 

27.7293123 

27.9604032 

28.1853092 

28.4041958 

28.6172241 

28.8245510 

29.0263290 

29.2227066 

29.4138284 

29.5998350 

29.7808633 

29.9570466 

30.1285146 

30.2953934 

30.4578058 

30.6158715 

30.7697067 

30.9194247 

31.0651356 

31.2069467 

31.3449624 

31.4792843 

31.6100112 


236 





TABLE VII 


R^te,AMi%t6SV2% 
Year*, ^ 38 to 50 


ACTUAL VALUE OF A SEMI-ANNUITY 


The actual value of a semi-annuity, or a semi-annual instalment of $1 payable 
for one to one hundred semi-annual periods, at a fixed rate of compound discounts 


Y o *• o Semi-Annual 
1 Cctib Instalments 


38 

76 


77 

39 

78 


79 

40 

80 


81 

41 

82 


83 

42 

84 


85 

43 

86 


87 

44 

88 


89 

45 

90 


91 

46 

92 


93 

47 

94 


95 

48 

96 


97 

49 

98 


99 

50 

100 




36.2522025 

36.4324735 

36.6087777 

36.7812023 

36.9498328 

37.1147525 

37.2760432 

37.4337847 

37.5880552 

37.7389310 

37.8864867 

38.0306955 

38.1719288 

38.3099565 

38.4449469 

38.5769669 

38.7060818 

38.8323556 

38.9558507 

39.0766284 

39.1947483 

39.3102690 

39.4232477 

39.5337403 

39.6418016 


5 % 


33.8757804 

34.0251491 

34.1708747 

34.3130460 

34.4517497 

34.5870704 

34.7190906 

34.8478907 

34.9735494 

35.0961432 

35.2157469 

35.3324334 

35.4362739 

35.5573378 

35.6656928 

35.7714050 

35.8745388 

35.9751572 

36.07332144 

36.16909146 

36.26252568 

36.35368098 

36.44261294 

36.52937580 

36.61402250 


5V2<fo 


31.7372393 

31.8610623 

31.9815713 

32.0988551 

32.2129999 

32.3240897 

32.4322063 

32.5374293 

32.6398361 

32.73950215 

32.83650069 

32.93090319 

33.02277905 

33.11219601 

33.19921981 

33.28391453 

33.36634245 

33.44656432 

33.52463917 

33.60062434 

33.67457589 

33.74654816 

33.81659418 

33.88476548 

33.95111226 


237 




R.te, 6 % to 7 % 
Years 1 to 12 


TABLE VII 


ACTUAL VALUE OF A SEMI-ANNUITY 


The actual value of a semi-annuity, or a semi-annual instalment of $1 payable 
for one to one hundred semi-annual periods, at a fixed rate of compound discount. 


V/»!a,rcs Semi-Annual 
i Cdiib Instalments 



1 

1 

2 


3 

2 

4 


5 

3 

6 


7 

4 

8 


9 

5 

10 


11 

6 

12 


13 

7 

14 


15 

8 

16 


17 

9 

18 


19 

10 

20 


21 

11 

22 


23 

12 

24 


25 


6 % 


0.9708737 

1.9134697 

2.8286113 

3.7170983 

4.5797071 

5.4171923 

6.2302845 

7.0196942 

7.7861117 

8.5302064 

9.2526282 

9.9540085 

10.6349605 

11.2960790 

11.9379414 

12.5611090 

13.1661260 

13.7535213 

14.3238080 

14.8774844 

15.4150343 

15.9369274 

16.4436199 

16.9355544 

17.4131608 


6 %% 


0.9685229 

1.9065599 

2.8150701 

3.6949831 

4.5471987 

5.3725889 

6.1719986 

6.9462453 

7.6961212 

8.4223929 

9.1258041 

9.8070734 

10.4668984 

11.1059541 

11.7248939 

12.3243515 

12.9049398 

13.4672533 

14.0118667 

14.5393371 

15.0502042 

15.5449909 

16.0242031 

16.4883312 

16.9378496 


7 % 


0.9661837 

1.8996944 

2.8016380 

3.6730808 

4.5150548 

5.3285562 

6.1145479 

6.8739608 

7.6076925 

8.3166122 

9.0015591 

9.6633437 

10.3027943 

10.9205324 

11.5174243 

12.0941314 

12.6513363 

13.1896987 

13.7098554 

14.2124225 

14.6979947 

15.1671467 

15.6204334 

16.0583918 

16.4815400 


238 




TABLE VH 


Rate, 6% to 7% 
Years, 13 to 2S 


ACTUAL VALUE OF A SEMI-ANNUITY 


The actual value of a semi-annuity, or a semi-annual instalment of $1 payable 
for one to one hundred semi-annual periods, at a fixed rate of compound discount. 


V*ao**o Semi-Annual 
1 cars Instalments 


13 

26 


27 

14 

28 


29 

15 

30 


31 

16 

32 


33 

17 

34 


35 

18 

36 


37 

19 

38 


39 

20 

40 


41 

21 

42 


43 

22 

44 


45 

23 

46 


47 

24 

48 


49 

25 

50 


6 % 


17.8768564 

18.3270463 

18.7641238 

19.1884710 

19.6004587 

20.0004467 

20.3887847 

20.7658118 

21.1318576 

21.4872418 

21.8322749 

22.1672586 

22.4924855 

22.8082397 

23.1147973 

23.4124260 

23.7013860 

23.9819296 

24.2543021 

24.5187414 

24.7754786 

25.0247380 

25.2667374 

25.5016884 

25.7297961 


6 %% 


17.3732184 

17.7948832 

18.2032752 

18.5988123 

18.9818990 

19.3529273 

19.7122767 

20.0603149 

20.3973978 

20.7238702 

21.0400662 

21.3463093 

21.6429128 

21.9301800 

22.2084049 

22.4778721 

22.7388572 

22.9916273 

23.2364409 

23.4735485 

23.7031928 

23.9256085 

24.1410233 

24.3496574 

24.5517242 


7 % 


16.8903787 

17.2853921 

17.6670477 

18.0357972 

18.3920769 

18.7363084 

19.0688992 

19.3902432 

19.7007204 

20.0006985 

20.2905324 

20.5705652 

20.8411283 

21.1025419 

21.3551155 

21.5991480 

21.8349282 

22.0627352 

22.2828386 

22.4954989 

22.7009679 

22.8994886 

23.0912961 

23.2766174 

23.4556718 


239 




date, 6% to 7% 
Ycar*» 26 to 37 


TABLE VII 

ACTUAL VALUE OF A SEMI-ANNUITY 


The actual value of a semi-annuity, or a semi-annual instalment of $1 payable 
for one to one hundred semi-annual periods, at a fixed rate of compound discount. 


Years 

Semi-Annual 

Instalments 

6% 


7% 


51 

25.9512599 

24.7474306 

23.6286712 

26 

52 

26.1662732 

24.9369767 

23.7958204 


53 

26.3750241 

25.1205565 

23.9573173 

27 

54 

26.5776949 

25.2983577 

24.1633529 


55 

26.7744626 

25.4705622 

24.2641120 

28 

56 

26.9654993 

25.6373462 

24.4097730 


57 

27.1509718 

25.7988803 

24.5505082 

29 

58 

27.3310422 

25.9553298 

24.6864843 


59 

27.5058678 

26.1068548 

24.8178622 

30 

60 

27.6756015 

26.2536102 

24.9447974 


61 

27.8403915 

26.3957461 

25.0674401 

31 

62 

28.0003813 

26.5334080 

25.1859355 


63 

28.1557117 

26.6667367 

25.3004238 

32 

64 

28.3065179 

26.7958686 

25.4110405 


65 

28.4529317 

26.9209358 

25.5179166 

33 

66 

28.5950810 

27.0420663 

25.6211785 


67 

28.7330900 

27.1593839 

25.72094842 

34 

68 

28.8670793 

27.2730087 

25.81734449 


69 

28.9971661 

27.3830570 

25.91048089 

35 

70 

29.1234639 

27.4896412 

26.00046777 


71 

29.2460832 

27.5928705 

26.08741159 

36 

72 

29.3651311 

27.6928504 

26.17141527 


73 

29.4807116 

27.78968329 

26.25257829 

37 

74 

29.5929256 

27.88346816 

26.33099669 


75 

29.7018713 

27.97430092 

26.40676326 


240 




TABLE VII 


Rate, 6% to 7% 
Years, 38 to 50 


ACTUAL VALUE OF A SEMI-ANNUITY 

The actual value of a semi-annuity, or a semi-annual instalment of $1 payable 
for one to one hundred semi-annual periods, at a fixed rate of compound discount. 


Years 

Semi-Annnal 

iDstalments 

6% 


79fc 

38 

76 

29.8076438 

28.06227458 

26.47996768 


77 

29.9103355 

28.14747908 

26.55069658 

39 

78 

30.0100362 

28.23000157 

26.61903368 


79 

30.1068330 

28.30992651 

26.68505988 

40 

80 

30.20081057 

28.38733558 

26.74885334 


81 

30.29205086 

28.46230805 

26.81048955 

41 

82 

30.38063368 

28.53492062 

26.87004143 


83 

30.46663638 

28.60524755 

26.92757948 

42 

84 

30.55013418 

28.67336081 

26.98317182 


85 

30.63120004 

28.73933004 

27.03688425 

43 

86 

30.70990474 

28.80322274 

27.08878030 


87 

30.78631708 

28.86510427 

27.13892139 

44 

88 

30.86050380 

28.92503794 

27.18736688 


89 

30.93252978 

28.98308505 

27.23417412 

45 

90 

31.00245796 

29.03930506 

27.27939854 


91 

31.07034938 

29.09375542 

27.32309361 

46 

92 

31.13626339 

29.14649186 

27.36531109 

93 

31.20025756 

29.19756830 

27.40610093 

47 

94 

31.26238783 

29.24703701 

27.44551142 

95 

31.32270850 

29.29494858 

27.48358919 

48 

96 

31.38127225 

29.34135203 

27.52037931 

97 

31.43813026 

29.38629483 

27.55592533 

49 

98 

31.49333222 

29.42982298 

27.59026931 

99 

31.54692635 

29.47198099 

27.62345189 

50 

100 

31.59895952 

29.51281200 

27.65551237 


21 


241 





Rate, 7V2%to8y2% 
Years, 1 to 12 


TABLE VII 

ACTUAL VALUE OF A SEMI-ANNUITY 


The actual value of a semi-annuity, or a semi-annual instalment of $1 payable 
for one to one hundred semi-annual periods, at a fixed rate of compound discount. 


Years 

Semi-Annual 

Instalments 

7%% 

8^0 

8%% 


1 

0.9638552 

0.9615384 

0.9592324 

1 

2 

1.8928726 

1.8860946 

1.8793598 


3 

2.7883106 

2.7750910 

2.7619762 

2 

4 

3.6513832 

3.6298958 

3.6086102 


5 

4.4832608 

4.4518236 

4.4207290 

3 

6 

5.2850702 

5.2421388 

5.1997400 


7 

6.0578987 

6.0020575 

5.9469924 

4 

8 

6.8027937 

6.7327483 

6.6637814 


9 

7.5207647 

7.4353360 

7.3513487 

5 

10 

8.2127853 

8.1109008 

8.0108853 


11 

8.8797929 

8.7604825 

8.6435344 

6 

12 

9.5226915 

9.3850804 

9.2503920 


13 

10.1423528 

9.9856553 

9.8325095 

7 

14 

10.7396166 

10.5631311 

10.3908958 


15 

11.3152931 

11.1183965 

10.9265179 

8 

16 

11.8701620 

11.6523055 

11.4403041 


17 

12.4049751 

12.1656795 

11.9331445 

9 

18 

12.9204577 

12.6593086 

12.4058934 


19 

13.4173084 

13.1339518 

12.8593691 

10 

20 

13.8962010 

13.5903396 

13.2943578 


21 

14.3577841 

14.0291739 

13.7116131 

11 

22 

14.8026836 

14.4511302 

14.1118580 


23 

15.2315023 

14.8568572 

14.4957861 

12 

24 

15.6448215 

15.2469796 

14.8640624 


25 

16.0432016 

15.6220973 

15.2173247 


242 





TABLE VII 


Rate,7y2Xto8y2^ 
Years, 13 to 25 


ACTUAL VALUE OF A SEMI-ANNUITY 


The actual value of a semi-annuity, or a semi-annual instalment of $1 payable 
for one to one hundred semi-annual periods, at a fixed rate of compound discount. 


Semi-Annual 
1 Cdib Instalments 


13 

26 


27 

14 

28 


29 

15 

30 


31 

16 

32 


33 

17 

34 


35 

18 

36 


37 

19 

38 


39 

20 

40 


41 

21 

42 


43 

22 

44 


45 

23 

46 


47 

24 

48 


49 

25 

50 


7 %% 


16.4271824 

16.7972844 

17.1540091 

17.4978402 

17.8292437 

18.1486687 

18.4565482 

18.7532995 

19.0393248 

19.3150119 

19.5807345 

19.8368526 

20.0837135 

20.3216517 

20.5509897 

20.7720384 

20.9850974 

21.1904554 

21.3383909 

21.5591721 

21.7630576 

21.9402966 

22.1111294 

22.2757875 

22.4344941 


8 % 


15.9827874 

16.3296047 

16.6630829 

16.9837350 

17.2920546 

17.5885157 

17.8735745 

18.1476696 

18.4112225 

18.6646388 

18.9083082 

19.1426059 

19.3678921 

19.5845134 

19.7928032 

19.9930818 

20.1856575 

20.3708264 

20.5488734 

20.7200725 

20.8846870 

21.0429703 

21.1951658 

21.3415075 

21.4822208 


8V2‘to 


15.5561856 

15.8812320 

16.1930270 

16.4921119 

16.7790030 

17.0541983 

17.3181745 

17.5713891 

17.8142808 

18.0472704 

18.2707616 

18.4851416 

18.6907819 

18.8880388 

19.0772540 

19.2587554 

19.4328575 

19.5998619 

19.7600579 

19.9137231 

20.0611238 

20.2025153 

20.3381426 

20.4682408 

20.5930352 


243 




Rate, 71 / 2 % to 8 V 2 % 
Years, 26 to 37 


TABLE VII 

ACTUAL VALUE OF A SEMI-ANNUITY 


The actual value of a semi-annuity, or a semi-annual instalment of $1 payable 
for one to one hundred semi-annual periods, at a fixed rate of compound discount. 


Years 

Semi-Annual 

Instalments 


8% 

8%% 


51 

22.5874643 

21.6175221 

20.7127420 

26 

52 

22.7349055 

21.7476194 

20.8275687 


53 

22.8770175 

21.8727130 

20.9377142 

27 

54 

23.0139929 

21.9929954 

21.0433693 


55 

23.1460174 

22.1086515 

21.1447171 

28 

56 

23.2732699 

22.2198593 

21.24193322 


57 

23.3959229 

22.3267898 

21.33518609 

29 

58 

23.5141427 

22.4296076 

21.42463727 


59 

23.6280895 

22.52847097 

21.51044177 

30 

60 

23.7379177 

22.62353189 

21.59274825 


61 

23.8437762 

22.71493663 

21.67169934 

31 

62 

23.9458085 

22.80282583 

21.74743179 


63 

24.04415289 

22.88733467 

21.82007681 

32 

64 

24.13894268 

22.96859321 

21.88976026 


65 

24.23030634 

23.04672641 

21.95660287 

33 

66 

24.31836768 

23.12185450 

22.02072051 


67 

24.40324608 

23.19409308 

22.08222422 

34 

68 

24.48505666 

23.26355326 

22.14122057 


69 

24.56391020 

23.33034189 

22.19781181 

35 

70 

24.63991359 

23.39456173 

22.25209595 


71 

24.71316984 

23.45631157 

22.30416706 

36 

72 

24.78377829 

23.51568645 

22.35411536 


73 

24.85183462 

23.57277768 

22.40202739 

. 37 

74 

24.91743110 

23.62767308 

22.44798619 


75 

24.98065664 

23.68045712 

22.49207136 


244 





TABLE VII 


IUte,7J/3%to8Va% 
Years 38 to 50 


ACTUAL VALUE OF A SEMI-ANNUITY 


The actual value of a semi-annuity, or a semi-annual instalment of $1 payable 
for one to one hundred semi-annual periods, at a fixed rate of compound discount 


Y#»are Semi-Annual 
1 Cdib Instalments 


38 

76 


77 

39 

78 


79 

40 

80 


81 

41 

82 


83 

42 

84 


85 

43 

86 


87 

44 

88 


89 

45 

90 


91 

46 

92 


93 

47 

94 


95 

48 

96 


97 

49 

98 


99 

50 

100 


23 




25.04159692 

25.10033456 

25.15694916 

25.21151742 

25.26411333 

25.31480819 

25.36367069 

25.41076717 

25.45616127 

25.49991465 

25.54208657 

25.58273412 

25.62191258 

25.65967494 

25.69607239 

25.73115429 

25.76496816 

25.79755984 

25.82897351 

25.85925174 

25.88843558 

25.91656458 

25.94367687 

25.96980920 

25.99499697 


8fo 


23.73121102 

23.78001284 

23.82693768 

23.87205770 

23.91544234 

23.95715832 

23.99726986 

24.03583865 

24.07292404 

24.10858306 

24.14287058 

24.17583937 

24.20754011 

24.23802161 

24.26733075 

24.29551262 

24.32261058 

24.34866630 

24.37371989 

24.39780988 

24.42097333 

24.44324588 

24.46466179 

24.48525402 

24.50505424 


8 %% 


22.53435929 

22.57492325 

22.61383352 

22.65115752 

22.68695992 

22.72130275 

22.75424552 

22.78584529 

22.81615681 

22.84523260 

22.87312305 

22.89987647 

22.92553923 

22,95015579 

22,97376878 

22,99641914 

23,01814610 

23,03898731 

23.05897887 

23.07815542 

23.09655019 

23,11419505 

23.13112058 

23,14735610 

23,16292974 


245 







^te, 9% to 10^ 
Yc«ra, 1 to 12 


TABLE VII 


Actual value of a semi-annuity 


The ^tual value of a Semi-annuity, or a semi-annual instalment of $1 payable 
for one to one hundred semi-annual periods, at a fixed rate of compound discount. 


Years 

Sbmi-Annual 
Instalments 


1 

1 

2 


3 

2 

4 


5 

3 

6 


7 

4 

8 


9 

5 

10 


11 

6 

12 


13 

7 

14 


15 

8 

16 


17 

9 

18 


19 

10 

20 


21 

11 

22 


23 

12 

24 


25 


9^0 


0.9569377 

1.8726677 

2.7489643 

3.5875263 

4.3899782 

5.1578739 

5.8927024 

6.5958874 

17.2687919 

7.9127196 

8.5289183 

9.1185823 

9.6828538 

10.2228267 

10.7395469 

11.2340162 

11.7071925 

12.1599928 

12.5932946 

13.0079373 

13.4047247 

13.7844254 

14.1477754 

14.4954786 

14.8282090 


91/2% 


0.9546540 

1.8660182 

2.7360554 

3.5666400 

4.3595884 

5.1165536 

'5.8391936 

6.5290648 

7.1876528 

7.8163767 

8.4165904 

8.9895871 

9.5366005 

10.0588090 

10.5573376 

11.0332599 

11.4876009 

11.9213395 

12.3354096 

12.7307034 

13.1080723 

13.4683290 

13.8122495 

14.1405748 

14.4540116 


10 % 


0.9523809 

1.8594103 

2.7232479 

3.5459503 

4.3294765 

5.0756918 

5.7863731 

6.4632124 

7.1078214 

7.7217347 

8.3064140 

8.8632514 

9.3935728 

9.8986407 

10.3796578 

10.8377692 

11.2740659 

11.6895866 

12.0853205 

12.4622099 

12.8211522 

13.1630021 

13.4885734 

13.7986413 

14.0939440 


246 




TABLE VH 

ACTUAL VALUE OF A SEMl-ANNUITY 


Rate. 9% to 10% 
Year., 13 to 25 


The actual value of a semi-annuity, or a semirannual instalment of $1 payable 
for one to one hundred semi-annual periods at a fixed rate.of compound discount 


Years 

Semi-Annual 

Instalments 

9% 

91 / 2 % 

10% 

13 

26 

15.1466113 

14.7532362 

14.3751847 


27 

15.4513026 

15.0388913 

14.6430330 

14 

28 

15.7428732 

15.3115931 

14.8981266 


29 

16.0218881 

15.5719289 

15.1410729 

15 

30 

16.2888880 

15.8204596 

15.3724503 


31 

16.5443903 

16.0577204 

15.5928098 

16 

32 

16.7888901 

16.2842224 

15.8026759 


33 

17.0228611 

16.5004534 

16.0025485 

17 

34 

17.2467569 

16.7068793 

16.1929033 


35 

17.4610112 

16.9039445 

16.3741936 

18 

36 

17.6660392 

17.0920735 

16.5468510 


37 

17.8622383 

17.2716717 

16.7112866 

19 

38 

18.0499886 

17.4431259 

16.8678920 


39 

18.2296540 

17.6068053 

17.0170399 

20 

40 

18.4015826 

17.7630625 

17.1590856 


41 

18.5661076 

17.9122340 

17.2943672 

21 

42 

18.7235477 

18.0546412 

17.4232068 


43 

18.8742081 

18.1905908 

17.5459112 

• 22 

44 

19.0183808 

18.3203756 

17.6627725 


45 

19.1563451 

18.4442752 

17.7740690 

23 

46 

19.2883683 

18.5625565 

17.8800657 


47 

19.4147063 

18.6754742 

17.9810086 

24 

48 

19.5356039 

18.7832715 

18.07715099 


49 

19.6512954 

18.8861806 

18.16872089 

25 

50 

19.7620049 

18.98442325 

18.25592461 


247 





Rale, 9% to 10^ 
"Years, 26 to 37 


TABLE VII 


ACTUAL VALUE OF A SEMIANNUITY 


The actual value of a semi-annuity, or a semi-annual instalment of $1 payable 
for one to one hundred semi-annual periods, at a fixed rate of compound discount. 


Years 

Semi-Annua 

Instalments 

9%' ' 

9^270 

107 o 


51 

19.8679470 

19.07821094 

18.33897577 

26 

52 

19.9693270 

19.16774576 

18.41807211 


53 

20.0663410 

19.25322052 

18.49340196 

27 

54 

20.1591777 

19.33481936 

18.56514468 


55 

20.2480166 

19.41271803 

18.63347107 

28 

56 

20.33303002 

19.48708428 

18.69854383 


57 

20.41438256 

19.55807836 

18.76051789 

29 

58 

20.49223188 

19.62585314 

18.88954079 


59 

20.56672882 

19.69055460 

18.87575309 

30 

60 

20.63801777 

19.75232209 

18.92928860 


61 

20.70623683 

19.81128867 

18.98027481 

31 

62 

20.77151822 

19.86758135 

19.02883310 


63 

20.83398848 

19.92132139 

19.07507909 

32 

64 

20.89376865 

19.97264454 

19.11912289 


65 

20.95097453 

20.02160130 

19.16106937 

33 

66 

21.00571701 

20.06835717 

19.20101840 


67 

21.05810217 

20.11299283 

19.23906509 

34 

68 

21.10823148 

20.15560444 

19.27530003 


69 

21.15620210 

20.19628378 

19.30980950 

35 

70 

21.20210699 

20.23511848 

19.34267566 


71 

21.24603512 

20.27219220 

19.37397676 

36 

72 

21.28807161 

20.30758475 

19.40378734 


^3 

21.32829792 

20.34137241 

19.43217837 

37 

74 

21.36679199 

20.37362792 

19.45921744 


75 

21.40362842 

20.40442078 

19.48496893 


248 






TABLE VII 


Rate, 9% to 10% 
Years, 38 to 59 


ACTUAL VALUE OF A SEMl-ANNUITY 


The actual value of a semi-annuity, or a semi-annual instalment of $1 payable 
for one to one hundred semi-annual periods, at a fixed rate of compound discount.l 


Semi-Annual 
cars Instalments 


38 

76 


77 

39 

78 


79 

40 

80 


81 

41 

82 


83 

42 

84 


85 

43 

86 


87 

44 

88 


89 

45 

90 


91 

46 

92 


93 

47 

94 


95 

48 

96 


97 

49 

98 


99 

50 

100 


9 % 


21.43887859 

21.47261081 

21.50489044 

21.53578004 

21.56533947 

21.59362600 

21.62069444 

21.64659726 

21.67138465 

21.69510464 

21.71780319 

21.73952429 

21.76031004 

21.78020070 

21.79923483 

21.81744930 

21.83487942 

21.85155896 

21.86752024 

21.88279419 

21.89741042 

21.91139724 

21.92478175 

21.93758989 

21.94984649 


91/2^0 


20.43381731 

20.46188082 

20.48867176 

20.51424783 

20.53866414 

20.56197327 

20.58422542 

20.60546852 

20.62574833 

20.64510853 

20.66359083 

20.68123503 

20.69807914 

20.71415944 

20.72951056 

20.74416557 

20.75815603 

20.77151208 

20.78426249 

20.79643472 

20.80805498 

20.81914831 

20.82973860 

20.83984867 

20.849500284 


10 % 


19.50949417 

19.53285153 

19.55509664 

19.57628246 

19.59645943 

19.61567559 

19.63397670 

19.65140633 

19.66800598 

19.68381517 

19.69887154 

19.71321094 

19.72686751 

19.73987377 

19.75226068 

19.76405774 

19.77529304 

19.78599332 

19.79618406 

19.805889529 

19.815132833 

19.823935979 

19.832319927 

19.840304641 

19.847909128 


249 






Rate,10y2%loll% 
Years, 1 to 12 


TABLE VII 


ACTUAL VALUE OF A SEMI-ANNUITY 


The actual value of a semi-annuity, or a semi-annual instalment of $1 payable 
for one to one hundred semi-annual periods, at a fixed rate of compound discount. 


Years 

Semi-Annual 

Instalments 

10V2% 

11% 


1 

0.9501187 

0.9478672 

1 

2 

1.8528443 

1.8463194 


3 

2.7105409 

2.6979328 

2 

4 

3.5254546 

3.5051494 


5 

4.2997195 

4.2702834 

3 

6 

5.0353630 

4.9955289 


7 

5.7343116 

5.6829652 

4 

8 

6.3983959 

6.3345635 


9 

7.0293549 

6.9521922 

5 

10 

7.6288409 

7.5376222 


11 

8.1984238 

8.0925321 

6 

12 

8.7395952 

8.6185131 


13 

9.2537722 

9.1170732 

7 

14 

9.7423015 

9.5896420 


15 

10.2064624 

10.0375744 

8 

16 

10.6474704 

10.4621549 


17 

11.0664803 

10.8646008 

9 

18 

11.4645895 

11.2460661 


19 

11.8428405 

11.6076445 

10 

20 

12.2022239 

11.9503728 


21 

12.5436808 

12.2752338 

11 

22 

12.8681054 

12.5831588 


23 

13.1763473 

12.8750308 

12 

24 

13.4692137 

13.1516867 


25 

13.7474716 

250 

13.4139198 




TABLE VII 


R»le,10i4%toll% 
Year*, 13 to 25 


ACTUAL VALUE OF A SEMI-ANNU1TY\ 


The actual value of a semi-annuity, or a semi-annual instalment of $1 payable 
for, one to one hundred semi-annual periods, at a fixed rate of compound discount. 


Years 

Semi-Annual 

Instalments 

10^2% 

life 

13 

26 

14.0118497 

13.6624820 


27 

14.2630403 

13.8980859 

14 

28 

14.5017012 

14.1214071 


29 

14.7284574 

14.3330860 

15 

30 

14.9439027 

14.5337295 


31 

15.1486013 

14.7239128 

16 

32 

15.3430893 

14.9041813 


33 

15.5278760 

15.0750520 

17 

34 

15.7034453 

15.2370147 


35 

15.8702570 

15.3905338 

18 

36 

16.0287479 

15.5360495 


37 

16.1793331 

15.6739791 

19 

38 

16.3224069 

15.8047180 


39 

16.4583440 

15.9286412 

20 

40 

16.5875004 

16.0461039 


41 

16.7102143 

16.1574430 

21 

42 

16.8268071 

16.2629776 


43 

16.9375841 

16.3630104 

22 

44 

17.0428354 

16.45782822 


45 

17.1428367 

16.54770294 

23 

46 

17.23784979 

16.63289224 


47 

17.32812349 

16.71364038 

24 

48 

17.41389423 

16.79017888 


49 

17.49538663 

16.86272723 

25 

50 

17.57281410 

16.93149342 


251 





IUle,10y2%toll.®^ 
Y^arty 26 to 37 


TABLE VII 


ACTUAL VALUE OF A SEMI-ANNUITY 


The actual value of a semi-annuity, or a semi-annual instalment of $1 payable 
for one to one hundred semi-annual periods, at a fixed rate of compound discount. 


Years 

Semi-Annual 

Instalments 

10%% 

11% 


51 

17.64637939 

16.99667465 

26 

52 

17.71627516 

17.05845779 


53 

17.78268444 

17.11702000 

27 

54 

17.84578114 

17.17252920 


55 

17.90573049 

17.22514455 

28 

56 

17.96268949 

17.27501692 


57 

18.01680732 

17.32228930 

29 

58 

18.06822568 

17.36709724 


59 

18.11707922 

17.40956922 

30 

60 

18.16345589 

17.44982702 


61 

18.20759724 

17.48798606 

31 

62 

18.24949876 

17.52415577 


63 

18.28931018 

17.55843985 

32 

64 

18.32713576 

17.59093660 


65 

18.36307455 

17.62173921 

33 

66 

18.39722067 

17.65093599 


67 

18.42966354 

17.67861067 

34 

68 

18.46048812 

17.70484259 


69 

18.48977513 

17.72970696 

35 

70 

18.51760127 

17.75327508 


71 

18.54403941 

17.77561453 

36 

72 

18.56915879 

17.79678936 


73 

18.59302518 

17.81686029 

37 

74 

18.61570109 

17.83588486 


75 

18.63724589 

252 

17.85391763 




TABLE VII 


Rate, 10%% to 11%- 
Years, 38 to 50 


ACTUAL VALUE OF A SEMI-ANNUITY 


The actual value of a semi-annuity, or a semi-annual instalment of $1 payable 
for one to one hundred semi-annual periods, at a fixed rate of compound discount. 


Semi-Annual 
1 Cctib Instalments 


38 

76 


77 

39 

78 


79 

40 

80 


81 

41 

82 


83 

42 

84 


85 

43 

86 


87 

44 

88 


89 

45 

90 


91 

46 

92 


93 

47 

94 


95 

48 

96 


97 

49 

98 


99 

50 

100 


10 %% 


18.65771601 

18.67716505 

18.69564395 

18.71320110 

18.72988248 

18.74573177 

18.76079048 

18.77509805 

18.78869194 

18.80160775 

18.81387930 

18.82553873 

18.83661657 

18.84714184 

18.85714209 

18.866643519 

18.875671005 

18.884248189 

18.892397533 

18.900140377 

18.907496999 

18.914486664 

18.921127674 

18.927437423 

18.933432434 

253 


11 % 


17.87101030 

17.88721189 

17.90256884 

17.91712519 

17.93092268 

17.94400087 

17.95639725 

17.96814737 

17.97928493 

17.98984186 

17.99984842 

18.009333314 

18.018323734 

18.026845460 

18.034922924 

18.042579287 

18.049836502 

18.056715348 

18.063235610 

18.069415951 

18.075274094 

18.080826837 

18.086090099 

18.091078972 

18.095807762 








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INDEX 


COMPOUND INTEREST 

Algebraic Solution ,... 
Arithmetical Solution . 


Page 

ft 


Compounding semi-annually, quarterly and monthly. ** 

Definition of compound interest . ** 

Solution by the tables . “ 

Accrued amount .“ 

Capital . ** 

Period of time . “ 

Rate of interest . " 

Table of the accrued amount of $1 from 1 to 100 years 
or periods, at to 10% compound interest. Table I... 


COMPOUND DISCOUNT 

Algebraic Solution _ 

Arithmetical Solution . 


Definition of Compound Discount . 

Solution by the tables .. 

The Capital or Actual Value .. 

of an amount ..... 

payable by instalments . 

of an annuity ... 

of a semi-annuity .. 

Table of the actual value, or the capital of an amount of $1, 
payable after 1 to 100 years, at 1% to 9^% compound dis¬ 
count, Table V . 

Table of the actual value, or the capital of an annuity of $1, 
payable for 1 to 100 years, at 1% to 9^% compound dis¬ 
count, Table VI . 

Table of the actual value, or the capital of a semi-annuity of $1, 
payable for 1 to 100 semi-annual periods at l^%toll% com¬ 
pound discount. Table VII ... 


1 to 4 
2 
1 

3, 4 
1 
2 

1 . 2 
2, 5 
3 
3 

1 to 61 
S to 7 
2, 5 
2 

5 

5, 6 

6 

5. 6 
6 
7 
7 


157 to 189 


191 to 223 


225 to 253 


ANNUITIES . “ 

Annuities for Investment or Sinking Funds . “ 

Accumulated amount, . “ 

of a capital and an annuity . ** 

Actual value of an annuity and a remaining amount. “ 

Algebraic equations of annuities . “ 

Solution . “ 

Annuity, Definition of . “ 

When there is a remaining amount . “ 

Investment, or Sinking Fund . “ 

At the beginning of every year. “ 

End of every year . “ 

Period of time . “ 

Of a capital, an annuity and a remaining amount 


8 to 21 
8 to 15 
10 
12 
13 
11 
9 
8 

13 
9 
9 
9 

14 
14 


255 






































Rate of interest... 

Of a capital, an annuity and a remaining amount 
Reasons for constructing Table II by making the investment 

at the end of every year .. 

Remaining amount after payment of annuities. 

Annuities for Instalment and Amortization. 

Algebraic solution . 

' Amortization, definition, of ... 

Quota ... 

Taliular illustration of ... 

Annuity Arithmetical process .. 

EquaTannual instalment . 

Of a premium ..1 

Capital . 

Period of time . 

Rate of interest .. 

Relation between the various tables. 

Remaining amount due . 

Semi-annuities or semi-annual instalments . 

Tabular illustration of amortization of premiums ... 
Table of the accumulated amount of $1 payable after 1 to 100 

years at 1 % to compound interest: Table’ll. 

Table of the annuity of a capital of $1 payable for 1 to 100 

years at 1 % to 9 ^% compound interest. Table III . 

Table of the semi-annuity of a capital of $1 payable for 1 to 100 
semi-annual periods at 1J4% to 7% compound interest. 

Table IV. 

LOANS . 

Loans issued at par .•. 

Amortization quota of, bonds . 

Capital . 

Definition of. Face value. 

Loan . 

Market price . 

Nominal value . 

Rate of issue .. 

Redemption price . 

Securities . 


Page 


<( 


« 


u 


« 


« 


if 


« 


Tabular illustration of a loan . “ 

The U. S. of America Loan . “ 

Loans issued at a different rate than par and redeemed at 

par . “ 

Amortization quota of, bonds . “ 

Capital . “ 

Amortized bonds after a number of years . “ 

Annuity or equal annual instalment . “ 

Capitalization rate, . “ 

After payment of a number of annuities “ 

At different market prices . “ 

Capital, nominal . “ 

Real or effective . “ 

Interest, real or effective rate* of . “ 

Tabular illustration of a loan . “ 

Loans redeemed above par . “ 


11, 10 

15 

9 

12 

16 to 21 

16 
16 
18 

. 18 
17 

17 

18 
20 
20 
21 
16 
27 
21 
19 

63 to 99 
101 to 137 


139 to 155 
22 to 48 
22 to 25 
23 

23 
22 - 
22 
22 
22 
22 
22 
22 ; 

24 
24, 25 

26 to 31 
27 
26 

27 
26 

28 
28, 29 

29 

26 

26 

29 

29, 30, 31 
32 to 38 


256 














































When the premiam ig etmstant..... ' .. ■ ; ^. Page 

Annuity .. . ................. . “ 

Bonds, face value . “ 

Market value .... ... ** 

Kumber to be st. ** 

Redemption value . “ 

Capital, nominal ...^..... i i... i^“ 

Real or effective . “ 

Capitalization rate . “ 

Tabular illustration of amortization quota . “ 

When the premium varies .. “ 

Amortization of bonds. . . . .. ” 

Annuity .. “ 

Calculations of charts of loans .. “ 

Definition of a premium . “ 

Tabular illustration . ” 

U. S. of America Loan .... ** 

Loans redeemed at par with premiums or prizes . ” 

Feature: of lottery privileiges . ** 

When the‘ yearly premium is divided equally among the 

bonds “to be redeemed . ** 

Annuity of, capital . “ 

* Premium ... “ 

Capitalization rate .. “ 

Real rate of interest ... “ 

When the yearly premium is given in the form of prizes to only 

a certain number of bonds to be redeemed . “ 

Amount of bonds to be issued .. ** 

Annuity . “ 

Nominal capital ... “ 

Primed bonds . “ 

Prizes, account of ... “ 

Real value of . “ 

When the premium is given to a fixed number of bonds in the 

form o( untqual prizes ... “ 

Amortiaatibil, talculation of .... “ 

•' Table Of .... “ 

Bonds, issued . ‘‘ 

Primed . 

Conditions of a loan . 

Table of prizes . “43, 

INCOME RATE OF AN INVESTMENT . “ 

When the redemption date is known . “ 

Bond, net income rate of . “ 

Parities .;.. “ 

Algebraic solution of . 

Solution by the tables of . 

Substitution of the premium by increasing the annual income “ 
The purchase price of a bond at a fixed income rate. ** 

Solution, Algebraic . “ 

By the tables . 


32 to 44 
33 

32 

33 

32 

33 
32 

32 

33 
33, 34 

34 to 38 
36 
35 
35 

34 
37, 38 

36, 37, 38 
39 to 48 

39 

40, 41 

40 

40 

41 

41 

41, 42 

42 
42 
42 
41 
41 

41 

42 to 48 
46 
47. 48 
46 

42 
46 

44, 45. 48 
49 to 57 
49 to 53 
49 

52 

49 

53 

50 

51 

51 

52 


257 

















































r r-redemption date is not known .. . ,Page 54 to 57 

V , Bonds,. Amortized ... ** 

Irredeemable ........ “ _ 54 

Date, Average or Mathematical .. “ 56 

Probable ...... “ 57 


PARITIES .*...;;. y.. ^.. “ 58 to 60 

' Basis, the real or effective rate of interest"......... . .58 

Determination of parity in loans of different classes ... 60 

'Loans on amortization plan, difference in the approximation 60 

. . Purchase price of a bond .tv*... ** . ; • 

The more advantageous investment between two bonds 

on the amortization plan........“ 58 


FARM LOANS .. ** 

Annual amortization quota ... ** 

Arithmetical solution of amortization ‘. ** 

Contraction of the farmers’ credit ... . .. ** 

Elasticity of credit to the farmers.•••••.•. ** 

Expansion of the farmers’ credit...... “ 

Extracts from the Federal loan act, bonds ... ** 

Mortgages ........... “ 

Federal Farm Loan Board ... ** 

Land banks ... 

Find the annuity or equal annual instalment .. “ 

Capital that may be borrowed ... “ 

New annuity after a partial anticipated payment.. . “ 

Period of time.... “ 

> Rate of interest... 

Remaining amount due after a payment of a num¬ 
ber of annuities . “ 

Semi-annuity or equal semi-annual instalment. “ 

Issue of farm loan bonds . “ 

Method of procedure in obtaining farm loans .. “ 

National Farm Loan Associations .“ 


Security of farm loan bonds . 

Semi-annual amortization quota . 

Tabular illustration of annual amortization . 

Semi-annual amortization 


61 to 70 

63 

64 
70 
70 
70 

. 69 

61 
61 
62 
63 

67 

^ 69 

-. 67 

68 

68 
65, 68 

69 
62 
62 

70 

65 

65 

66 



258 


































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